CHICAGO (CBS) — Bears general manager has proved he’s not afraid to move up in the NFL Draft to pick a player he wants, after trading up twice in the past two years, but don’t expect the Bears to trade up into the first or second round this year.

“That would be tough, It would be hard, just because we don’t have a lot of ammunition,” Pace said Tuesday at Halas Hall.

The Bears traded away their first and sixth round draft picks in the 2019 draft as part of the deal to acquire stud pass rusher Khalil Mack from the Raiders last year. They also traded their second round pick to move up and draft wide receiver Anthony Miller.

As it stands, the Bears won’t make their first draft pick until the third round, number 87 overall. Pace said he’s confident the Bears can get a player capable of starting in Week One in the middle rounds of the draft, but his focus as always is on picking the best player available, even if it’s not a position of need.

“If we take a player where we happen to have a lot of depth right now, but it’s a good player, that’s okay. I think it’s short-sighted to say this guy might be able to play a little bit quicker, so let’s take him. Let’s just take the best player. If that means it takes a little longer for him to play, let’s just make sure we pick the best guy.”

Even with the Bears having only five picks this year, fewer than any other NFL team except the Seattle Seahawks, Pace said he feels just as much pressure as any other draft.

“I feel like, with fewer picks, and with later picks, the onus is on us as scouts to hit on these picks, and to keep this momentum. I feel like we had momentum. To keep this momentum going, we have to nail this draft,” Pace said.

Pace said his staff typically compiles a “cloud” of players worth drafting when their pick comes up, and with so many picks before the Bears get their first turn with the 87th pick overall, that cloud is bigger than usual.

“There’s this bigger pool of players that we’re talking about. And there’s certain players where we could say, ‘God, man, if this guy, we valued him so high, if he’s falling to this point, we will consider going up for him,’ or ‘Hey, there’s enough good guys, we’re going to stay right here,’ or if they’re all coming off, maybe we back it up,” he said.

One advantage to not picking until the third round could be that Ryan has had more time to research mid- and late-round prospects than years past.

“I would say I’ve spent more time in the mid-round area of this draft than I have in the past,” Pace said.

Pace also said it’s an especially deep draft, with a record number of underclassmen coming out of college this year.

“We are in a good position to be picking where we’re picking. We feel very certain that we can get a good player at our picks,” he said.

The Bears might get the chance to take one position off the draft board, after former Bears kicker Robbie Gould pulled out of contract talks with the 49ers, and asked to be traded. The 49ers placed the franchise tag on Gould in February, but the veteran kicker reportedly grew weary of long-term contract talks going nowhere, and wants to be closer to his wife and family in Chicago.

The Bears likely will at least make a pitch to the 49ers to acquire him, given the three kickers currently signed by the team – Redford Jones, Chris Blewitt, and Elliot Fry – have no NFL experience.

Word of Gould’s trade demand came after Pace had completed his pre-draft press conference, so it’s unclear what inquiries the Bears have made, if any, regarding Gould’s availability in a trade.