Frank Lampard is looking to make several additions to an Everton squad that barely managed to survive in the Premier League last season.
The Everton boss is aware of the financial restrictions his side are working under but is looking at several potential new signings.
And it has been claimed that the Everton boss wants Walker-Peters as part of his plans to strengthen his Everton squad.
Lampard lost Jonjoe Kenny this summer and Nathan Patterson has struggled to nail down a spot in the team.
He wants a new right-back and Walker-Peters has emerged as one of the top targets for Everton.
Southampton are claimed to want around £10m to £15m before they would agree to sell the former Tottenham defender.
Walker-Peters could be open to a move to Merseyside and Everton and Southampton will hold talks over the coming days to agree on a fee.
The 25-year-old was a key player for the Saints last summer but the club may be prepared to sell him for the right price.