Mankins, who publicly asked to be traded last year, sounded hopeful that a long-term deal could be worked out, according to the Boston Herald.
"There's always a chance," Mankins, 29, said when asked about receiving a long-term deal from the Patriots. "I've talked to the coaches, ownership, everyone. We're all on the same page. We'll see happens.
"I have great memories here," Mankins added. "I've had a lot of fun. I like everyone here. We'll see what happens. I understand it's a business now more than ever. We'll see what happens."
Mankins, who signed his tender quickly this year instead of waiting as he did last year, smiled when asked about why he did it, saying: "I figured I'm getting paid a lot of money this year. I should put in a full year."
Mankins also was anxious to deny beliefs that he had a problem with Patriots owner Robert Kraft, stemming from his rant against the franchise for allegedly being misled about a new deal.
"Let's get things straight: Me and Mr. Kraft never had a problem," Mankins said when asked about his relationship with the owner. "I never said he lied. I think when I said the organization, I never said 'he' did. So let's get that straight right now.
"Me and Mr. Kraft never had a problem. We've talked last offseason, we've talked last season, we've talked this offseason, we've talked in training camp, so everything is good between me and him."
Mankins was even seen shaking hands and talking with Kraft on the field Thursday.