Tuilagi has reportedly held talks over a move to Paris when his Leicester Tigers contract expires at the end of the season.
On Thursday RugbyPass revealed that a deal with the Top 14 club has been completed, but there has been no official confirmation from the club or player.
The 27-year-old has forced his way into the England starting line-up after putting his injury woes behind him to make a long-awaited comeback last year, but a switch to the Top 14 would effectively make him unavailable for Test rugby.
England head coach Jones says only Tuilagi can decide what his future holds.
“As long as he doesn’t get on the Eurostar between now and Saturday I’ve got no comment on it because all I’m worried about is Saturday.
“I don’t decide what he does for his family. Every player has a family situation they have got to look after and I want them to look after their families.
“He is in our family at the moment and we want him to play well for us – that is our only concern right now. He’s got to make a decision and what decision he makes will be up to him. He’s a massively important part of our team. The guys like playing with him, they love him.
“He loves playing with the team and that is his only concern at the moment.”
Watch: Eddie Jones talks to RugbyPass ahead of Wales
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