The Jets entered the NFL draft on Thursday with one of their major offseason issues somewhat resolved and the other one still up in the air.

Defensive end Muhammad Wilkerson was not traded on draft night, making it a near certainty he will be on the Jets in 2016 either playing under the franchise tag or with a long-term deal.

“I would not envision a trade happening,” general manager Mike Maccagnan said after selecting Ohio State linebacker Darron Lee at No. 20.

However, the situation with free-agent quarterback Ryan Fitzpatrick remained unsettled and shows no signs of ending anytime soon. A report surfaced Thursday afternoon that Fitzpatrick would rather sit out this season than play for what the Jets are offering. A source told The Post that was not true, though, and Fitzpatrick still hopes to get a deal done with the Jets.

There may be some semantics at play here because it is clear Fitzpatrick does not want to play for what the Jets are offering, believed to have started in the $7 million-to-$8 million range and upped a little since then. Fitzpatrick is open to playing for another team, but no one has expressed interest in him at his asking price of around $16 million.

Fitzpatrick, 33, threw for a franchise-record 31 touchdowns last season after coming to the Jets in a trade with the Texans. He clicked with receivers Brandon Marshall and Eric Decker and thrived under offensive coordinator Chan Gailey, his former coach in Buffalo. Both sides said at the end of the season they wanted to stay together in 2016, but the negotiations have gone nowhere since they began two months ago.

Wilkerson is in a similar situation to Fitzpatrick in that he is unhappy with what the Jets are offering him as a long-term contract. The difference is the Jets used the franchise tag on Wilkerson, 26, to keep him under team control for 2016. He will earn $15.7 million under the tag.

With a long-term contract unlikely, though, the Jets were open to trading Wilkerson, something they made clear to other teams in the weeks leading up to the draft. But no team was willing to give the Jets what they were looking for (a first-round pick for starters) and Wilkerson what he wants in a long-term contract (around $50 million guaranteed). A deal would have had to have been reached before the draft began because Wilkerson’s agent would need to negotiate with the team trading for him before a deal would be agreed to and the team getting Wilkerson would want to give him an extensive physical to check how the leg he broke in the season finale is healing.

There remains a minuscule chance the Jets could trade him after the draft, but player-for-player trades in the NFL are rare and the team acquiring Wilkerson would again have to be willing to give him a long-term contract.

While Wilkerson surely is unhappy that he was not moved because he has grown tired of the Jets dragging their feet on a contract, the Jets should be happy they have Wilkerson for another season. He is the team’s best defensive player and is coming off a Pro Bowl season.

The Wilkerson and Fitzpatrick situations have been the biggest story lines of the Jets’ offseason. The Wilkerson one will quiet for now. The team has until July 15 to work out a long-term deal with him, so tune back in then.

But the Fitzpatrick story drags on. It was unthinkable in February that Fitzpatrick would be unsigned at the draft. But as Roger Goodell opened the draft on Thursday, that was the case.

Marshall testified before a Senate Finance Committee hearing on mental health on Tuesday. Marshall was diagnosed with borderline personality disorder in 2011 and since has done work to increase awareness of mental health issues. He is the chairman of Project 375, which tries to reduce the stigmas surrounding mental illness.