"Make sure the length of his contract is a lot shorter than mine," Umenyiora told Sirius XM NFL Radio, via the New York Daily News, on Monday.
2012's notable free agents
Umenyiora signed a seven-year, $41.38 million contract in 2005 -- a deal that became a source of tension between he and the team before the start of the 2011 season. Cruz broke out for a record-setting season in 2011, but is scheduled to make $490,000 next season and is left hoping for a new contract.
Umenyiora wants Cruz to avoid the mistakes he made if he re-negotiates his contract during the offseason.
"I basically signed like an eight-year deal," Umenyiora said. "You sign an eight-year deal, your career is pretty much (over) before you're able to actually get back to free agency. Things in the NFL change so fast. One time you're being highly paid, and then the next year you're one of the lowest paid players in the league."
Umenyiora has one more year left on his contract, and while he said he'd be open to a return to New York, he told ESPN Radio's "Mike and Mike in the Morning" that a trade wouldn't surprise him.
"We're just going to have to wait and see," Umenyiora said, via ProFootballTalk.com. "I can see it going either way. I can see where they would keep me, I can see where they would trade me, because it makes sense both ways. So hopefully things will work out in my interest.
"I know the team is going to do what's best for them. They've always made the right decisions for that organization. Whether that's keeping me or trading me, I'd love to stay, but at the end of the day I understand it's a business and hopefully things will work out."