McCoy grew up in Texas and starred at the University of Texas in Austin from 2006 to 2009.
"I think it's great," Browns general manager Tom Heckert said at his Thursday morning pre-draft news conference. "If they do it, great. If they don't do it, I don't think it's a big deal. They'll be ready when it's time to go."
Players and coaches haven't been permitted to have any contact since league owners imposed a lockout March 12. According to The Plain Dealer, McCoy was given a copy of new coach Pat Shurmur's playbook before the lockout began.
And by this time next week, McCoy might have new targets.
With the No. 6 overall pick in next week's draft, the Browns could have the chance to add a top-flight wide receiver such as Georgia's A.J. Green or Alabama's Julio Jones, considered the top two prospects at that position. It's possible one or both could be available when it's Cleveland's turn on the clock.
Since trading Braylon Edwards to the New York Jets in 2009, the Browns have lacked a home-run-hitting receiver, the kind of player who can turn a 10-yard reception on a slant pattern into a 70-yard touchdown. Massaquoi and Robiskie are suitable, and both made significant strides in their second seasons as pros.
However, the Browns need more to develop McCoy, who will run a new West Coast offense installed by Shurmur.
Green or Jones would fill a gaping hole.
Heckert said Thursday there is little difference between the two Southeastern Conference stars.
"They are both very talented guys," he said. "They are both good football players. They both can run and catch and all that stuff. I think some people might like something else about one guy than the other guy. If you talk to 32 teams, you'll probably get 16 answers to why one guy might do something better.
"At that position, it's a little hard because they are both kind of the same size and maybe one runs a little faster but they are very similar players. There's not much difference as an overall package."
Asked which was better suited for the West Coast offense, Heckert said, "either one is fine."
As for the upcoming draft, Heckert didn't tip his hand as to what the Browns will do with their top pick. In his first draft with Cleveland last year, Heckert took cornerback Joe Haden at No. 7, added safety T.J. Ward in the second round (No. 38) and grabbed McCoy (No. 85) after he slid to the third.
Heckert addressed several draft-related topics:
» On Clemson defensive end Da'Quan Bowers' surgically repaired knee; Bowers could be an option for the Browns, who are shifting to a 4-3 front: "Our doctors have looked at him 100 times," Heckert said. "We've done our due diligence. We think his knee is going to all right."
» On North Carolina defensive end Robert Quinn being a high risk after his one-season NCAA suspension for receiving gifts and travel accommodations: "Obviously, it's a thing you'd rather not have to deal with. You'd like to see him play this year, and unfortunately you can't. ... You have one less year to look at for him. You just have to kind of use your judgment."
» On the possibility of trading up: "It's probably unlikely, but I have talked to some teams ahead of us just to see. That's probably a tougher thing to do from our situation. We'd hate to give up picks to do something like that."
» On LSU cornerback Patrick Peterson, considered by many a can't-miss pick: "Size and speed. He's a rare guy, a rare athlete and he's a very good football player."
» On if Browns president Mike Holmgren has veto power on quarterbacks; Holmgren allegedly was the one who persuaded Heckert to choose McCoy: "That's completely not true. Colt McCoy was the guy that was there when we picked. He was our highest-rated guy. Did Mike like him? Yes. Did I like him? Yes. Did Eric (Mangini) like him? Yeah. That's blown a little bit out of proportion."
The Associated Press contributed to this report.