Though Cleveland fans may already be clamoring to see McCoy play, Holmgren cautions that it would be a mistake to put him on the field before he's ready.
Holmgren said he made a phone call to the Rams 20 minutes before the draft began on Thursday and offered a package for the No. 1 pick.
Instead, he waited it out and took McCoy 85th. Oklahoma quarterback Sam Bradford was chosen first overall by St. Louis.
Holmgren said he made the offer to Rams general manager Billy Devaney "at the limits of what I was willing to do."
Holmgren says Devaney "finally said we're going to take him [Bradford]." Holmgren would not specify what he offered the Rams.
Information from The Associated Press was used in this report.