The request to the Premier League has been passed to both the English FA and football's world governing body FIFA who will have the final say on whether to waive the rules in a move that could help Portsmouth survive.
"FIFA can confirm it has received correspondence from the FA relating to the financial situation at Portsmouth FC and the proposed measures to be taken in this respect," the governing body said in a statement.
FIFA will need to make a decision quickly if the proposed sales are to help Portsmouth who urgently need to raise funds so they can pay off some of their bills and creditors.
A spokesman for the club said: "I can confirm we have put in a request to the Premier League to sell players outside the transfer window. It is something we are exploring."
The winter transfer window was open from January 1 to February 1 and clubs cannot sell players again until the next window opens after the end of this season.
Portsmouth, bottom of the Premier League, face a winding-up petition from the Government's Revenue and Customs office over an unpaid tax bill of 11.7 million pounds on March 1.
The club, which say two interested parties are potential buyers, lodged a Statement of Affairs with the High Court in London on Wednesday to prove they are still a solvent company.
If Portsmouth are wound-up the players contracts cease to be assets of the club and it would also lose its membership of the Premier League.
That would have a huge impact on the competition, with the points clubs have won against them this season deducted from their current totals.
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