When it comes to the possibility of the Bears selecting a quarterback early in the draft next month, new starter Mike Glennon heard all he needed to hear from general manager Ryan Pace last week.

‘‘All I can do is control what I can control,’’ Glennon said. ‘‘I heard Ryan say I’m the starting quarterback, and I’m going to work with all the guys to be the best player I can be.’’

Of the Bears’ eight free-agent signees thus far, Glennon is by far the most important. But whether he knows it or not, his arrival does affect the team’s draft plans.

The Bears’ goal for free agency was to improve their roster to the point where they don’t feel compelled to reach on a player because of a position of need, and they’ve done that. As Pace has said plenty of times, the Bears will be built through the draft.

With the first and second waves of free agency complete, here are the Bears’ top five draft needs:

1. Edge rusher

The Bears have five outside linebackers on their roster: Leonard Floyd, Pernell McPhee, Willie Young, Lamarr Houston and Roy Robertson-Harris. So it’s a thin position.

Floyd, the Bears’ first-round pick last year, is the only contributor who won’t be returning from surgery. (Robertson-Harris spent his rookie season on the reserve/non-football illness list.) So it’s an embattled position.

The Bears can release McPhee and Houston without major salary-cap implications. So it’s an intriguing position.

It wasn’t a great year for edge rushers in free agency, but this draft class is considered special for them.

Texas A&M’s Myles Garrett is by far the best, but he’s projected to go first overall to the Browns. It would be a gift from the football gods if Garrett somehow fell to the Bears at No. 3.

But the draft class is deep enough that talented threats can be found on the second day. Players to watch include Michigan’s Taco Charlton, UCLA’s Takkarist McKinley, Wisconsin’s T.J. Watt, Alabama’s Tim Williams, Auburn’s Carl Lawson and Illinois’ Dawuane Smoot.

In general, the Bears’ defensive front needs an upgrade. That’s why defensive linemen Jonathan Allen (Alabama) and Solomon Thomas (Stanford) are considered possibilities at No. 3.

2. Quarterback

The Bears think Glennon is much more than a backup, but they still protected themselves by structuring his contract the way they did.

Glennon signed a three-year, $45 million deal, but his total guarantee is $18.5 million — $16 million of which will come this season. His contract also includes incentives for victories and individual performance.

In other words, for as much as the Bears rave about Glennon, they still want him to earn their long-term commitment.

That said, it’s unfair to describe Glennon as a ‘‘bridge’’ quarterback. He’s a 27-year-old with upside who deserves a serious chance in 2017 and also 2018.

But Glennon’s arrival doesn’t mean the Bears won’t pick a quarterback early on; it means they don’t have to force the pick. That’s very important. The last thing Pace wants to do is reach on a quarterback during a draft year that’s widely considered average for them.

Quarterbacks to watch include Pittsburgh’s Nate Peterman, Cal’s Davis Webb and Miami’s Brad Kaaya.

3. Safety

The Bears signed veteran safety Quintin Demps to a three-year, $13.5 million contract, but the details of the deal are revealing.

Demps only has a total guarantee of $5 million, so he essentially has a one-year deal. His contract also includes roster bonuses of $31,250 per game over every year of the deal, so he needs to play to get paid.

But Demps still has value. The Bears hope he can be the reliable veteran Antrel Rolle wasn’t in 2015 because of injuries and ineffectiveness. They need Demps’ presence on and off the field to matter more.

After Demps, the Bears have Deon Bush, Adrian Amos, Harold Jones-Quartey and DeAndre Houston-Carson. All four can benefit from being around a seasoned veteran.

But the Bears can turn to the draft for help at safety. It’s a special year for them, too.

The Bears could strike early by taking LSU’s Jamal Adams or Ohio State’s Malik Hooker at No. 3. Traditionally, that’s early to select a safety. But the value of safeties has been rising with the changes in offensive schemes and the widespread use of pass-catching tight ends.

4. Receiver

Adding Markus Wheaton and Kendall Wright was important. The Bears wanted speed at receiver, and now they have it.

But the Bears’ commitments to them are limited. Wright got only a one-year deal. Wheaton signed for two years, but only 2017 is guaranteed. There are also bonuses included for receptions and receiving yards.

With Wright and Wheaton on the roster, though, the Bears won’t feel pressured to reach to replace Alshon Jeffery. The thought is that both might thrive when given more significant roles.

Wright and Wheaton also will provide insurance should Cam Meredith struggle to duplicate his success from last season or if Kevin White needs more time to come back from his second major surgery on his lower leg.

5. Cornerback

Prince Amukamara (one-year, $7 million contract) and Marcus Cooper (three-year, $16 million contract, including $8 million guaranteed) make cornerback the Bears’ deepest position, but that depth always can be improved.

The draft class for cornerbacks is exceptional. Some evaluators have said possible mid-round selections would have been higher selections in previous drafts.

‘‘I can get through four rounds of quality corners,’’ NFL Network analyst Mike Mayock said. ‘‘I’ve never been able to say that before.’’

The Bears’ depth also can become thin quickly because of injuries and personnel moves. Kyle Fuller already is on shaky ground, and Tracy Porter can be let go without major salary-cap consequences.