Contrary to a report on Thursday afternoon, there has been no transaction to this point involving Red Sox reliever Takashi Saito, according to a major-league source. Specifically, as of Thursday afternoon, he has not been assigned outright to Pawtucket or removed from the 40-man roster.

That said, it would not come as a surprise if the Sox were to attempt to outright Saito in the coming days for the purposes of making him a free agent, since doing so would give the club its best opportunity to re-sign the pitcher as a free agent. Here’s how:

For the team to attempt an outright assignment, Saito would have to be placed on and clear outright waivers. Assuming that he went unclaimed, Saito — as a player with 3+ years of major-league service time — would have the right to elect free agency. The pitcher unquestionably would exercise that right. That, in turn, would make him an unrestricted free agent, eligible to re-sign with any of the 30 MLB teams, including the Red Sox.

The Sox hold a $6 million option (with an additional $1.5 million in potential incentives) on Saito for the 2010 season. As WEEI.com reported earlier this month, a clause in Saito’s contract required the Sox to release the pitcher if they did not exercise their option. If the Sox simply release Saito without outrighting him, however, they would be ineligible to re-sign Saito until May 15. Free agency resulting from an outright assignment, on the other hand, would put the Sox on a level playing field with the other 29 teams in bidding for the pitcher’s services.

Saito went 3-3 with a 2.43 ERA in 56 appearances for the Sox this year, striking out 52 and allowing 50 hits in 55.2 innings. The Sox signed him to a base salary of $1.5 million with numerous incentives last offseason, and those incentives ultimately increased the value of both his 2009 earnings and his 2010 option to $6 million.

Though the Sox almost certainly will not exercise the pitcher’s 2010 option, the possibility remains that the team could seek to re-sign Saito for a lower base salary. The right-hander, who will be 40 next season, said that he would like to return to pitch in the majors again in 2010, and that he would like to return to the Sox.

“Since it’s something I can’t control, I can’t say much, but I’m hoping to come back to America and pitch again, and [would like] especially to come back to the Red Sox,” Saito said in late-September.