The team has aggressively examined the market but have been put off by high asking prices, Howe adds.
The club reached out to the Detroit Lions and Philadelphia Eagles regarding Matthew Stafford and Carson Wentz, respectively, but weren't considered prime suitors for the now-traded quarterbacks. Stafford reportedly told the Lions he would be accepting of a trade to any team but the Patriots.
New England hasn't ruled out the possibility of bringing back Cam Newton, who is scheduled to be a free agent, Howe notes.
Newton, who completed his first season in New England, also expressed interest in a return.
"Yes. Hell yes. I'm getting tired of changing. I'm at the point in my career where I know way more than I knew last year," Newton said on the "I Am An Athlete" podcast, according to Chris Mason of Mass Live.
The 31-year-old signal-caller was signed to a one-year deal during last year's offseason as the team searched for a replacement for Tom Brady. The former Carolina Panthers quarterback struggled with an offense that finished 27th in scoring. Newton completed 65.8% of his passes, tossing eight touchdowns to 10 interceptions with 12 rushing scores.
The Patriots finished 7-9 last season, missing the playoffs for the first time since 2008.