"Could we? In theory? Yes," Brown said Wednesday at the team's pre-draft news conference. "But are we planning on it or is that the plan? No."
Brown was even asked if he had the Patriots on speed dial.
"We do not," he said.
These statements should quell lingering speculation that the Browns are pursuing a trade for Garoppolo or the Bengals' AJ McCarron.
The Browns, who have the No. 1 overall pick, will look to the draft to improve the position, and may find themselves with Brock Osweiler on the roster as well.
The Browns took Osweiler -- and his $16 million guaranteed salary -- from Houston in March as part of a trade that also provided a second-round pick in 2018.
Brown said the team will not announce before draft night whom it will select first, but he did say the team has narrowed down its options and received calls about a possible trade for the No. 1 pick. However, it did not sound like he envisioned trading down.
"We feel really good about picking at one, and I'll leave it at that," Brown said.
The Browns twice traded down in the draft a year ago and wound up going from the second overall pick to 15th, where they selected receiver Corey Coleman.
"That would surprise me if we trade down in that fashion," Brown said.
"Positive young man," Brown said of Trubisky. "Bright, very competitive, brings a lunch box, blue-collar mentality to the position. We were impressed by him."
The Browns also have the 12th overall pick, and they possibly could use that as trade bait to move up and take Trubisky if they select Garrett at No. 1. The Browns have 11 picks in this draft, which makes a trade up easier to complete.
"We don't want to make a habit of turning two picks into one, but we're positioned to do it,'' Brown said.