The Toffees had agreed a €32m (£29m/$37m) deal with Barcelona to sign Yerry Mina, only for talks between the club and player's representatives to have dragged, with Lyon having now emerged as a potential suitor.
And the protracted move for Mina compounds what has been a difficult summer for Marco Silva in his attempts to bring in a top-quality central defender.
Aside from their interest in Mina, Everton had also looked at bringing in Marcos Rojo from Manchester United although there has been no additional movement over a possible deal for the Argentine.
Silva will now consider an approach for Frenchman Zouma, who spent the 2017-18 campaign on loan with relegated Stoke City and is not part of new boss Maurizio Sarri's first-team plans at Stamford Bridge.
Indeed, Zouma has trained away from the first team with the club's group of loan players during pre-season and appears certain to be moved on before the transfer window closes at 5pm BST on August 9.
Despite struggling to break through at Chelsea in recent years, Zouma is still considered one of the Premier League's top young defenders and was part of France's B list for the World Cup.
As well as the 23-year-old, Chelsea could also allow Tammy Abraham to leave on loan, with the striker having attracted interest from Championship club Aston Villa.
The Blues would prefer the England forward to make the move to a Premier League club, however, while Michy Batshuayi is another who could be offloaded, with Sevilla leading the race to sign him on loan.
Everton, meanwhile, face a race against time to get any final deals over the line, with Thursday's transfer deadline fast approaching and Lucas Digne and Richarlison the only significant additions having been made by the club so far.
They have, however, agreed a deal to bring Brazil international Bernard to Goodison Park on a free transfer after he left Shakhtar Donetsk.
Additional reporting by Neil Jones and Ignasi Oliva