The Browns told Njoku, 23, that they would like to keep him, but Rosenhaus told the team he's intent on a trade.
"It is in David's best interest to find a new team at this time," Rosenhaus told Schefter.
The Browns have known for about a year that Njoku would welcome a trade, a source told ESPN's Jeremy Fowler.
Sources with other teams told Fowler that Njoku might be worth a fourth- or fifth-round pick.
The Browns announced in April that they would pick up Njoku's fifth-year option, worth $6.4 million.
They had already signed Pro Bowl tight end Austin Hooper to a four-year, $44 million deal with $23 million guaranteed in March. Then they drafted tight end Harrison Bryant in the fourth round of the 2020 draft. But new coach Kevin Stefanski values tight ends and said after the draft he could see all three playing.
Njoku, a 2017 first-round pick out of Miami, broke his wrist and suffered a concussion in Week 2 of the 2019 season. He played only two more games after that and finished the season with five receptions for 41 yards and one touchdown.
In 2018, he had 56 receptions for 639 yards and four touchdowns.