The Titans, Browns, Chargers, Cowboys, Jaguars, Ravens, 49ers, Dolphins, Buccaneers and Giants make up the top 10 teams in the 2016 NFL Draft, but only a few have been rumored to select a passer.
In the top five, Dallas and Cleveland have been connected to quarterbacks, but there have been recent developments on that front.
Cowboys owner Jerry Jones said the team will "unequivocally not take a quarterback at No. 4," according to NFL Media's Gil Brandt.
Dallas has Tony Romo, but there were concerns about his ability to be available, as the 35-year-old only played in four games last season due to injury, and hasn't completed a full 16-game slate since 2012.
The Browns, also in the top 10, picking at No. 2 overall, are expected to select one of the top quarterbacks in this year's class, which is headed by California's Jared Goff and North Dakota State's Carson Wentz.
And while fans have their favorite and draft experts have expressed their opinions on who the Browns should take, Jackson said the team isn't close to making a choice.
"But obviously I know that that's the most important position everybody is talking about," said Jackson, hired by Cleveland in January after two seasons as Cincinnati's offensive coordinator. "So we'll spend the time grinding on our quarterbacks, grinding on every position that's there. We're not anywhere close to being able to make a decision on what is best for us right now."
Associated Press contributed to this report