The 21-year-old has previously admitted that he is ready to move on and his club are reported to be prepared to listen to offers in the region of £13million.
Liverpool have long been linked with Sissoko, but there is said to be rivalry from Premier League competitors Newcastle and European heavyweights Inter Milan.
According to the powerful central midfielder's representative, Bacary Sanogo, Lyon are also hopeful of securing a deal in what is developing into at least a four-way battle.
"The link with Lyon is serious, but it is not the only one," Sanogo said in the Liverpool Echo.
"There are also negotiations with Liverpool, Newcastle and Inter. Things should seriously move next week.
"His priority is a club with a major sporting project."