But according to Jackson, who is 1-29 in two seasons in Cleveland, he's not going anywhere.
"I've kind of known about Marvin,'' Jackson said after the Browns' latest loss, a 27-10 effort against the Ravens. "Obviously, we all know that Marvin is a close friend, but trust me, I'm not running from this. I've never gone any place and left it worse than when I found it. I'm going to be here, and I need to get this fixed as fast as I can because it's important."
After going 1-15 in his inaugural season, Jackson is 0-14 in 2017.
"It is important to me to help these players, help this organization and this city become what I believe we can become," he continued. "I have too many things going on here. I can't worry about what's happening in Cincinnati."
And while Browns owner Jimmy Haslam has said that Jackson will be the coach in 2018, just-hired general manager John Dorsey didn't offer the same level of commitment in a recent radio interview.
"I've always said I live in the present, and I build for the future," Dorsey told ESPN Cleveland's Aaron Goldhammer. "I live in the present. Right now the sun's out, the tarps are coming off the field, we're practicing outside, we're getting ready to play the Baltimore Ravens, which is a divisional game. That's my sole focus. And then it's also getting familiar with the whole layout and the organizational structure in terms of creating my daily routine."
But according to Cleveland.com's Mary Kay Cabot, Dorsey and Jackson "are genuinely eager to work together and off to a great start," though there's also the possibility that Dorsey could look to bring in his own coach, as CBS Sports NFL Insider Jason La Canfora has reported.
Whatever happens, Jackson maintains that a) "John Dorsey being here is one of the catalysts to getting the organization back to where it needs to be," and b) losing will be a thing of the past.
"There's no way," Jackson said. "It can't. There's not a bone in my body that thinks this will ever be like this again. I know I said it a year ago that I didn't think it would be this way heading into next season -- it is. I was wrong. I'll be the first to tell you that and I will stand on that, but there is no way that this organization, this football team, this city, [the Haslams], the rest of the people in this organization can stomach this again. There's no way, and I know we won't."
Now the question is whether Jackson will be part of the solution in Cleveland or the rebuilding effort in Cincinnati.