BOSTON — This is how bad it has gotten for Carmelo Anthony and the Knicks:

Five months after swearing his allegiance to New York and signing a five-year, $124 million contract, sources told The Post the All-Star forward would be open to dropping his no-trade clause if team president Phil Jackson strikes a deal with a team Anthony would like to play for.

Part of Anthony’s deal included the rarely used no-trade provision.

For now, Anthony has no desire to be traded, but his willingness to consider giving up the no-trade clause shows how frustrated he has become with the Knicks’ historically bad start to the season.

The Knicks have lost 10 straight games — two shy of a team record — and at 4-20 have the most losses in the NBA, one more than the laughingstock Sixers.

On Wednesday, it was revealed Anthony got into an on-court scuffle with teammate Tim Hardaway recently, which resulted in a players-only meeting on Saturday.

Anthony can be traded beginning Monday — the unofficial start of trade season, when all free agents and draft picks signed over the summer can be moved.

A trade to a contender would be a financial boon to Anthony as he has a trade kicker attached to his contract that is worth 15 percent of the remaining value at the time of the deal. That kicker was put in place by Anthony’s handlers to deter teams from approaching the Knicks about Anthony. He would receive a lump-sum payment of roughly $17.5 million if he is traded Monday.

“He thought things would be better than this, but he still wants to stick it out for now, ’’ a source said. “He trusts Phil, but I think he’s afraid of Phil.’’

Instead of setting groundwork for a brighter future, the Knicks are off to their worst start in history, on pace to be the worst team in franchise history, and are looking as if they will battle Philly and Detroit for the lottery’s top seed. After Friday night’s game against the improved Celtics, the Knicks face a bruising slate the rest of December.

After re-signing with the Knicks this summer, Anthony said he didn’t want to experience another season like 2013-14, yet this is on pace to be far worse. He has said he will show patience, but indicated it would eventually run thin.

“I’m willing to be patient,” Anthony said Sept. 30. “Now, how long am I willing to be patient? I can’t tell you that. But I’m willing to be patient.”

Anthony’s big goal in free agency was signing with a team that could turn into a title contender. Even Jackson expressed fear Monday the current losing hurts his chances of landing a superstar free agent to play alongside Anthony when the Knicks have cap space in 2015.

It’s noteworthy that in June, Jackson tried to convince Anthony to opt into his previous contract so he and the team’s star could spend one season together to see if their marriage would work.

“I’ve told him it might be a good idea to hang in here and see what it’s like for a year,’’ Jackson said at the time. “I just offered that this gives you an opportunity to see how this is going to change, how we’re going to get it going.’’

Reports of a rift and the recent on-court incident with Hardaway do not help. The team held a players-only meeting Saturday, in which grievances were aired. Anthony said he wasn’t blamed in the meeting, but a report stated other Knicks approached him about his lack of passing and defense.

If Jackson looks to trade Anthony, the Bulls would be the obvious candidate. They pursued him heavily in the offseason, and the new documentary on his free agency tour depicted how close Anthony came to asking Jackson for a sign-and-trade to Chicago, since he didn’t want to accept the $74 million offer the Bulls had room for under the cap.

Anthony also visited Houston, Dallas and the Lakers.

Jackson could break up the team completely by trading Anthony for draft picks and expiring contracts. But Anthony would have to approve any deal.

The trade kicker doesn’t help his market value, nor does Anthony’s troubled knee.

Anthony said this week he may take a break to rest his sore left knee. He sat out Wednesday’s game in San Antonio, and it’s unclear if he’ll be available against the Celtics. He’s listed as day-to-day.

The Knicks are in such shambles, Jackson may have to simply make a trade — addition by subtraction. Jackson branded the Knicks as having “a loser’s mentality’’ down the stretch of games, and Anthony has missed a lot of big shots late in the fourth quarter during the current losing streak.

Jackson also criticized Anthony’s game for lacking more defensive energy and pluck on the offensive boards.

For his part, Anthony retorted, “We don’t have a loser’s mentality.’’