The Browns already have made a major trade this season, dealing Richardson to the Indianapolis Colts in exchange for a first-round draft pick.
If the Browns come up with the money it will take to land Tate, they would have him and Indianapolis' first-round draft pick in place of Richardson.
At least one team has made a quality offer for Gordon while another has weighed in on Little, a source said. Cleveland will not make any trades unless the offers for Gordon and Little improve, according to the source.
Browns CEO Joe Banner said that the Richardson trade, which was completed Wednesday, was not reflective of anything negative about the star running back, and that the team simply seized an opportunity to improve with the deal.
The Cleveland Plain Dealer reported the Browns initiated the Richardson trade, citing league sources.
Tate is sharing carries in Houston this season with Arian Foster and is running hungry, knowing full well the lucrative contract that could be awaiting him in free agency.
The 25-year-old Tate entered Sunday with 148 rushing yards on just 18 carries, averaging 8.2 yards per carry.
Gordon, 22, will make his season debut Sunday following a two-game suspension. The 24-year-old Little has struggled so far this season, averaging just 7.4 yards per reception.