"He just wasn't in the first batch of guys," Jackson told Cleveland.com at the Senior Bowl. "But he's definitely on our list."
Jackson did reach out to tackle Joe Thomas, who had said he might be wary of returning. Thomas has spoken positively of Jackson's hiring.
"I'm kind of really picking guys," Jackson told the website. "Some I know on this team that I've been involved with at other places. Some I don't know and want to get to know.
"There's no rhyme or reason why I haven't talked to [Manziel], but it's just the process I'm in right now. I'm just kind of picking the guys as I go."
Jackson said he did not want to "direct anything" at Manziel.
"I don't think that's the right thing to do," he said. "One of my philosophies for our organization is talent is important, but character and being a good person and doing the things that we want done as a Cleveland Brown is very important."
Manziel has appeared this week on various social media platforms out and about in Dallas. Jackson said he did not feel he needed to speak to Manziel about his offseason.
"One, I haven't watched it to be very honest with you," Jackson told 92.3 The Fan. "Then, No. 2, it is the offseason, and I would hope that players would do a great job of representing themselves and our organization and our team in a positive light. That's what we want.
"And if guys don't, I mean, I think everybody understands and recognizes there's consequences for everything that you do."
At the time of Jackson's hiring earlier this month, a source close to the situation told ESPN's Dan Graziano that the topic of Manziel was discussed at length in meetings between Jackson and Browns ownership. In those discussions, Jackson indicated that if he were to become head coach he would prefer that the organization part ways with Manziel, and Jackson was told that would not be a problem.