And if anyone thought that thought process would change once the Browns used the No. 1 overall pick in the NFL Draft to select Baker Mayfield, Jackson offered a reminder at the start of Cleveland's three-day minicamp.
"Tyrod Taylor's the starting quarterback of this football team, and that won't change," Jackson said Friday.
Mayfield, the Heisman Trophy-winning quarterback from the University of Oklahoma, certainly heard his coach's sentiments and understands Jackson's thinking, but he's not treating those words like gospel.
"I'm always competitive," Mayfield said on Saturday, per Cleveland.com. "It wouldn't matter what [Jackson] was saying in regards to the competition. I'm still going to compete and try and win that job. And so I'm going to listen to [Jackson], but I've got to go compete, and first and foremost, I've got to go learn my job."
The 28-year-old Taylor was among a series of moves made by Cleveland in the offseason, acquired in a trade with the Buffalo Bills in March.
Taylor guided Buffalo to the postseason for the first time since 1999 last season and already has drawn rave reviews from teammates along with an endorsement from Jackson.
Mayfield knows why Taylor has the backing of Jackson and noted that his goal is to make similarly favorable impressions with his new teammates.
"They brought him and I in because we're both team-oriented guys," said Mayfield. "He's the starter, and all I can do is help us out. So when you get a guy like that that helps out a locker room in just the best way possible, he's a grinder. He comes in early. He's the last one to leave, and I can only aspire to be like that."
Mayfield's stock improved dramatically leading up to the draft. NFLDraftScout.com's senior analyst Rob Rang initially projected Mayfield as the fourth quarterback to be taken, but moved him up to No. 1 in his final mock draft.
That doesn't mean there isn't a huge learning curve for Mayfield, who passed for 4,627 yards and accounted for 48 touchdowns with just six interceptions while leading Oklahoma to the College Football Playoff last season.
Mayfield has heard the concerns about his size (just under 6-foot-1) and ability to play over center, having taken the majority of snaps during his college career in the shotgun formation.
That's why there was an emphasis on both footwork and ball protection during the minicamp for Mayfield, who fumbled two snaps Friday and bobbled another Saturday, according to Cleveland.com.
"We've got to make sure we're not having to worry about that," said Mayfield of taking care of the ball. "Obviously, it puts you in position to turn the ball over, so [it's important we're] making sure we handle the basics first, and then you're able to move on and progress from there."
Jackson does not want to place inordinate expectations on Mayfield, who was sporting a bracelet with the inscription: "Humble Over Hype."
"He has a lot of characteristics that we love. That's why he's here," said Jackson. "[But] let's make sure we pump our brakes a little bit, because he's got a ways to go and a lot to learn. I'm very excited about him. It was a good first day, but he's got a ways to go. The guy you're comparing him to [Taylor] has played a lot of games, and won games in the National Football League."