Sunderland boss Steve Bruce has been a long-term admirer of the Ghana international and is now close to landing his man.
Mensah only joined Lyon last summer from Rennes, but is ready for a move to the Premier League, having also been linked with Portsmouth.
He has held talks with Sunderland and his representative Fabian Piveteau expects the centre-half to finalise his switch to the Stadium of Light at the start of next week.
"The deal is 95 per cent completed now and it will go through on Monday, I think," said Piveteau in the Sunderland Echo.
"The date of when it will be announced will depend on when he gets his visa, but it is close now.
"It is John's dream to play in England and he has been very impressed with Steve Bruce, with Eric Black and with Sunderland Football Club.
"He already has a good relationship with Steve and with Eric too, who knows the French game well and speaks fluent French.
"The deal is for one year with an option to signing at the end of that year. It is a good move for John because Sunderland are a big club with ambition."