Jackson said when it comes to the quarterback position, "There is no competition," according to NFL Network's Ian Rapoport.
The Browns also own the No. 1 and No. 4 overall picks in the 2018 NFL draft, and it is expected that they will select a quarterback with one of those choices.
Among the top options are USC's Sam Darnold, UCLA's Josh Rosen, Oklahoma's Baker Mayfield and Wyoming's Josh Allen.
Even if the Browns do take a signal-caller, Jackson's comments suggest he is happy to allow that quarterback to sit behind Taylor and learn for at least one season.
The 28-year-old Taylor spent the past three seasons as Buffalo's starter after a four-year stint as a backup for the Baltimore Ravens.
Taylor posted a 22-20 record, and he made one Pro Bowl during his time with the Bills.
Last season, Taylor completed 62.6 percent of his passes for 2,799 yards, 14 touchdowns and four interceptions. He also rushed for 427 yards and four touchdowns in 15 games, including 14 starts.
Most notably, Taylor helped the Bills end the NFL's longest playoff drought by reaching the postseason for the first time since 1999.
The Bills fell 10-3 to the Jacksonville Jaguars in the AFC Wild Card Round, as Taylor finished with just 134 passing yards and one interception in the game.
The Browns cycled through multiple quarterbacks last season with DeShone Kizer, Kevin Hogan and Cody Kessler all struggling en route to an 0-16 record.
Kizer was traded to the Green Bay Packers, meaning Taylor is the clear starter in terms of quarterbacks still on the roster.
Although Cleveland may find its long-term answer under center in the draft, Taylor will have another shot at being a starting NFL quarterback after seemingly falling out of favor in Buffalo.