Holmgren, speaking with some of the team's season-ticket holders on a conference call Thursday, said the Browns made a strong offer to St. Louis to try and get the No. 2 pick in next month's draft, a pick they would have used to select the Baylor quarterback and Heisman Trophy winner.
Reporters were unable to ask questions during the conference calls and the Browns have not made Holmgren or general manager Tom Heckert available to the media since their failed pursuit of Griffin.
"There are reasons it didn't happen," Holmgren said. "We were very aggressive and it didn't work. Rest assured, we were aggressively involved in that."
Holmgren said he still thinks McCoy can be a solid quarterback, mimicking Heckert's recent comments about the third-year QB, who had an inconsistent season.
Rucker agreed to terms on a five-year, $21 million contract Wednesday and signed his deal Thursday after passing a physical. The Cincinnati Enquirer reported the deal includes $8 million guaranteed.
Rucker had his best season with Cincinnati in 2011, recording a career-high four sacks in 11 starts. He appeared in all 16 games in helping the Bengals make the AFC playoffs.
"Frostee is a player that we targeted in free agency, and we couldn't be happier that he chose to become a member of the Cleveland Browns," Heckert said. "We really like the veteran presence that he will give our young defensive line. He started last year for one of the top defenses in the NFL, and we feel as though he can come in and have that same impact on our defense."
Cousins made one start at right tackle last season after the Browns were awarded him off waivers from Baltimore. He has made five career starts and played in 30 games. Cousins gives the Browns offensive line depth after the team released right tackle Tony Pashos, who recently underwent foot surgery and is expected to need 10 months to recover.
Smith made four starts last season. He finished with 14 catches for 131 yards and a touchdown.