Senate Democratic Leader Charles Schumer Chuck SchumerMcConnell accuses Democrats of sowing division by 'downplaying progress' on election security Warren, Schumer introduce plan for next president to cancel ,000 in student debt Schumer lashes out at Trump over 'blue states' remark: 'What a disgrace' MORE (D-N.Y.) is recruiting Rep. Ruben Gallego Ruben GallegoHispanic caucus report takes stock of accomplishments with eye toward 2021 Senators call on Pentagon to reinstate funding for Stars and Stripes newspaper Hispanic Caucus campaign chief to mount leadership bid MORE (Ariz.), a rising Democratic star in the House, to run for the Arizona Senate seat long held by John McCain John Sidney McCainThe electoral reality that the media ignores Kelly's lead widens to 10 points in Arizona Senate race: poll COVID response shows a way forward on private gun sale checks MORE.

Schumer and Democratic Senatorial Campaign Committee (DSCC) Chairwoman Catherine Cortez Masto Catherine Marie Cortez MastoVA problems raise worries about mail slowdown, prescriptions Cortez Masto touts mail-in voting in convention speech Vulnerable Senate Democrat urges unity: 'Not about what side of the aisle we're on' MORE (Nev.) met with Gallego at the DSCC headquarters Wednesday evening about running for the seat.

“It went great,” Gallego said of the meeting. “I’m strongly considering it.”

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“I’m basically making the final decision and we’ll have that in the next couple weeks,” he added.

Gallego, who was elected to his third House term in November, is the son of Hispanic immigrants, a Harvard graduate, and a Marine combat veteran who served in Iraq.

He serves as senior whip for the Democratic caucus, is the second vice chairman of the Congressional Hispanic Caucus, and vice chairman of the Congressional Progressive Caucus.

Schumer and Cortez Masto have also met recently with retired astronaut-turned-gun control advocate Mark Kelly and former Republican state attorney general Grant Woods, who are both mulling potential Senate bids, according to a DSCC aide.

Kelly, who once flew space shuttle missions for NASA, is the target of a draft campaign by 314 Action, a group trying to elect candidates with science, technology, engineering and math backgrounds to Congress.

The group is running a six-figure digital advertising campaign in an attempt to persuade Kelly to run.

Woods, who served as Arizona state attorney general in the 1990s, was McCain’s first congressional chief of staff in the 1990s.

He criticized the Republican Party in a September op-ed for azcentral.com for having abandoned its “tethering philosophy.”

He says he would run as a Democrat if he can’t do so as an independent.

The seat that McCain held for more than 30 years is currently occupied by Sen. Martha McSally Martha Elizabeth McSallyThe Hill's Campaign Report: Arizona shifts towards Biden | Biden prepares for drive-in town hall | New Biden ad targets Latino voters Biden leads Trump by 4 points in new Arizona poll Airline job cuts loom in battleground states MORE (R), who served two terms in the House before losing a hard-fought race for Jeff Flake Jeffrey (Jeff) Lane FlakeRepublican former Michigan governor says he's voting for Biden Maybe they just don't like cowboys: The president is successful, some just don't like his style Bush endorsing Biden? Don't hold your breath MORE’s (R) Senate seat to Kyrsten Sinema (D).

She was picked in December to serve the remainder of McCain's term.

Democrats see McSally as one of their top targets in 2020, along with Sens. Cory Gardner Cory Scott GardnerAirline job cuts loom in battleground states House approves bill to secure internet-connected federal devices against cyber threats Congress needs to finalize space weather bill as solar storms pose heightened threat MORE (R-Colo.) and Susan Collins Susan Margaret CollinsThe Hill's Campaign Report: Biden asks if public can trust vaccine from Trump ahead of Election Day | Oklahoma health officials raised red flags before Trump rally Gideon leads Collins by 12 points in Maine Senate race: poll Senate leaders quash talk of rank-and-file COVID-19 deal MORE (R-Maine), who are both running in states that Democratic presidential nominee Hillary Clinton Hillary Diane Rodham ClintonHillicon Valley: FBI chief says Russia is trying to interfere in election to undermine Biden | Treasury Dept. sanctions Iranian government-backed hackers The Hill's Campaign Report: Arizona shifts towards Biden | Biden prepares for drive-in town hall | New Biden ad targets Latino voters FBI chief says Russia is trying to interfere in election to undermine Biden MORE won in 2016.

Trump won Arizona in 2016 by 3.5 points but Sinema was able to defeat McSally by just over 2 points in November.

Arizona Gov. Doug Ducey (R) first appointed former Sen. Jon Kyl (R) to McCain's seat after McCain's death in August. Kyl stepped down, as planned, in December, following the midterms.

Democrats think McSally will be vulnerable in 2020, a presidential election year when Democratic turnout is usually higher, because of her embrace of Trump in the 2018 Senate GOP primary.

Mike Noble, an Arizona-based GOP pollster, told Reuters in August that embracing Trump in the primary “put McSally in a precarious position” but noted that it was necessary for her to advance to the general election.

Schumer played a key role in recruiting Sinema to run for the Senate in the 2018 cycle. He called her in August of 2017 to pledge his support over other primary candidates if she decided to run against Flake, who Democrats saw as vulnerable.

Flake announced his retirement in October of that year, denouncing the direction of the GOP under Trump.

At this point, however, it does not appear that Schumer is ready to clear the Arizona primary field for a favored pick as he is meeting with several candidates.

--Updated at 12:49 p.m.