Everton are exploring moves for Southampton's Mario Lemina and Chelsea's Fikayo Tomori, Sky Sports News understands.
The Toffees view Lemina as a potential replacement for Idrissa Gueye. Gueye is understood to be in the French capital to undergo a medical ahead of a permanent switch to Paris Saint-Germain.
Lemina has also attracted the attention of Wolves and Manchester United, and has been freed to speak to other clubs by the Saints this summer.
St Etienne are one of a number of clubs from France also keen, as well as further teams from Spain and Italy.
Everton are also in the market for a centre-back. Their first choice would be to re-sign Kurt Zouma but, with the deal stalling, they are considering England Under-21 international Tomori instead.
The 21-year-old spent last season on loan at Derby where he played under Frank Lampard, who is now in charge at Stamford Bridge.
Tomori is a product of the Chelsea academy and, having also spent time on loan at Brighton and Hull in the Championship, looks set for his first full season in the Premier League.