The Dolphins have been discussing the possibility of trading Bess for more than a month, Darlington reports, but they previously had not begun searching for suitors until very recently.
Citing a league source, Jensen added that several other teams are also in the mix. The Miami Herald's Armando Salguero reported Wednesday citing a source that among the teams the Dolphins called to see if they're interested in Bess are the Arizona Cardinals, St. Louis Rams, San Francisco 49ers, Minnesota Vikings and New York Jets.
The Dolphins are hoping to get mid-round draft pick in return.
Bess appeared in 15 games last season (13 starts), finishing with 61 catches for 778 yards and a touchdown. He became expendable when the Dolphins signed Brandon Gibson to a three-year contract last month.
The Browns have an existing option at the slot in free-agent wide receiver David Nelson. Still, Bess is a steady contributor who would add depth to the unit. He has one year left on his deal, meaning he'd likely get a new contract from whatever team acquires his services.
As for the Dolphins, this effort to move Bess could be a signal they are targeting West Virginia wide receiver Tavon Austin. Given Austin's sky-high stock, they'd likely have to trade up to have a shot.
Follow Dan Hanzus on Twitter @DanHanzus.