The market for left-hander Antonio Bastardo — arguably the top remaining free agent reliever on the market — has begun to pick up this week, per Baseball Essential’s Robert Murray. The Dodgers, Orioles, Mets and Blue Jays are all interested in Bastardo’s services, according to the report, which also notes that the Cubs met with Bastardo’s reps from the Legacy Agency at last month’s Winter Meetings.

Bastardo has reportedly been seeking a contract similar to the one secured by fellow free-agent lefty Tony Sipp this offseason. The 32-year-old Sipp landed a three-year, $18MM contract to return to Houston back in December, but the market for Bastardo’s services hasn’t been as aggressive despite the fact that he’s two years younger. While Murray notes that the intensifying market could potentially lead to a three-year pact, it’s difficult to see either the Mets or Blue Jays doling out that type of contract. The Mets are reportedly only interested in one-year deals with the remaining free agent relievers on the market, and the Blue Jays are said to be working with budgetary restrictions as their payroll is set to exceed last year’s mark as it is. The Orioles have been aggressive of late, but the $161MM they recently spent on Chris Davis (plus the $31MM given to Darren O’Day, the $7MM allotted to Korean outfielder Hyun Soo Kim and the $16.1MM going to Matt Wieters via the qualifying offer) calls into question how much more they’ll spend. (It’s also worth noting that with Brian Matusz, T.J. McFarland and closer Zach Britton, the team already has three lefties in the ’pen.)

The Dodgers, to be sure, have virtually unlimited spending capacity, but they’ve taken a surprisingly measured approach to their bullpen shopping this winter. The Cubs, theoretically, could issue that kind of deal, though Murray notes that it’s not clear when the last contact between the two sides even was, and they, too, have three lefties in the ’pen (Travis Wood, Clayton Richard, Rex Brothers).

Bastardo, 30, has been a somewhat quietly excellent performer across the past three seasons with the Phillies and Pirates. In that time, Bastardo has logged a 3.18 ERA with 10.5 K/9, 4.4 BB/9 and a 30.8 percent ground-ball rate. He’s also been effective against both left- and right-handed batters, holding same-handed opponents to a .167/.273/.295 batting line while surrendering just a .204/.310/.314 batting line even when his opponents hold the platoon advantage. Of course, control has been a persistent problem for Bastardo, too, as he’s only averaged less than four walks per nine innings in one season of his career — his debut campaign in 2009, when he tossed just 23 2/3 innings.