The Ivorian has been linked with both clubs this summer as they seek reinforcements.
According to the Daily Star, Seri has a £35 million release clause in his contract that is set to expire later this summer.
Chelsea's Kenedy has medical ahead of Newcastle loan return
During his time at Newcastle, Kenedy made 13 Premier League starts and became popular member of the side. Kenedy , 22, has travelled to Tyneside for a medical, having trained with Chelsea on Monday.
Chelsea are now in a predicament with their delay in recruiting Maurizio Sarri as their next head coach but they remain optimistic that a deal could be struck before they face Perth Glory in their opening pre-season game.
Seri has developed in to one of the best midfielders in French football since joining Nice from Pacos de Ferreira in 2015 and he was virtually ever-present last season as he provided 2 goals and 10 assists to help Nice finish 8th in the Ligue 1 table.