As we approach the holiday season, it’s time to think of St. John’s as the gift that keeps on giving. And that gift is agita.

The latest group suffering high blood pressure and a sick feeling in the belly is several Big East Conference coaches and assistants. Several told The Post they are outraged St. John’s is hoping to play in the league championship tournament after sanctioning itself last week.

“Your league championship is set up to determine who will represent you in the NCAA Tournament,” said one Big East coach. “Why should a school that has already said it won’t play in that tournament be included in the conference tournament?”

Last Friday, St. John’s announced that it was barring itself from post-season play for NCAA violations it uncovered. The most serious violation was a $300 monthly payment to former player Abe Keita.

St. John’s forwarded the results of its report to the NCAA, which will review it and decide what action to take. If St. John’s believes the NCAA will accept the university’s findings, it could be in for a shock.

A source with knowledge of how the NCAA works said the governing body for intercollegiate sports remains outraged by comments former coach Mike Jarvis made in the 1999-2000 season.

The NCAA was investigating an allegation of car-swapping involving Erick Barkley. Jarvis said he felt the NCAA – for the way it handled the investigation – had raped him.

Jarvis’ comments prompted an unusual and shocking response from then NCAA executive director Cedric Dempsey, who told St. John’s to tone down its rhetoric. Dempsey no longer is the NCAA’s executive director, but the investigator on the case, Deana Garner, remains with the NCAA.

“St. John’s was one of the most difficult, antagonistic institutions they [the NCAA] ever dealt with,” said the source. “I’m not saying the NCAA has a vendetta. I am saying it’s human nature to work with people who work with you and work against people who work against you.”

St. John’s (1-2), which played Stony Brook (2-1) last night at the newly named Carnesecca Arena, seems to be working against everyone these days. It did not inform the Big East that it was going to release the results of its inquiry until the middle of last week, just prior to the Thanksgiving holiday.

By waiting, St. John’s shoved the Big East between a rock and a hard place. After Syracuse, which was banned from postseason play in 1993 played in the Big East tournament (the Orangemen lost to Seton Hall in the championship game) the Big East instituted a policy under which any school banned from post-season play is banned from the Big East tournament.

If the league upholds that policy, the tournament will have to be reconfigured with one less game. TV monies probably will have to be returned. If the league presidents vote to include St. John’s, they’ll be reviewed as sellouts, who took the money over principle.

“Are they really considering it,” asked one assistant coach. “That’s bleep.”

A third coach was asked why it’s a big deal to allow St. John’s, which is coming off a 6-21 season and seemingly has no chance of winning the Big East tournament, to play.

“It doesn’t matter whether they have a chance or not,” said the coach. “It means that one team has to play another game, has to grind it out against a team that has nothing to lose. St. John’s brought this upon itself. It should pay the price.”