The midfielder is expected to sign for the Ligue 1 side on a two-year contract after leaving Real Madrid as a free agent.
But it was reported by the Daily Star that Ramos has rejected the possibility of joining United in favor of a move to Paris.
The Spaniard spoke to United chiefs about a possible move to the Premier League and Old Trafford before making his decision.
The Red Devils were prepared to offer him a one-year contract, with a one-second option, in a deal worth up to £ 10million.
Will Sergio Ramos regret snubbing Manchester United for the second time? Comments below
But that was not enough to convince Ramos to move to Manchester as Ole Gunnar Solskjaer now turns to his former team-mate Raphael Varane who is set to leave Madrid this summer.
And this is not the first time Ramos has refused to move to Man Utd.
He revealed he turned down an offer from United five years ago but was flattered that a club of their stature wanted to sign him.
In an interview with COPE, he said: “There was an offer from United. I considered changing for a while, but Real Madrid have always been my priority and there was no economic reason.
“Did I feel cheated [by Madrid]? No, but I was disappointed for a while. There were problems that ended.
“Big club flattery is always good because you are doing well, but the fans and my club want me. “