According to Dutch newspaper De Telegraaf, the Mexican midfielder refused to train with Ajax after the club recieved a €50 million bid from the Premier League club. The offer has reportedly unsettled Alvarez, who is trying to force a move to Stamford Bridge.
However, Telegraaf journalist Mike Verweij has now claimed that the Eredivise giants will not allow the Mexico international to leave this summer.
De Godenzonen have had their squad raided this summer, with no fewer than eight first-team players leaving the Johan Cruijff Arena in the transfer window. Sebastian Haller, Antony, Lisandro Martinez and Ryan Gravenberch are among those who have followed manager Erik ten Hag out of the exit door over recent months.
With N'Golo Kante and Jorginho both in the final years of their contracts, Chelsea are keen to strengthen in central midfield. The Blues' current alternatives in midfield include Conor Gallagher, Ruben Loftus-Cheek and Mateo Kovacic.
But following a slow start to the season, Thomas Tuchel will be keen to bring in a defensive midfielder, with his team keeping one clean sheet in five games so far.
Thomas Tuchel claims Chelsea need to toughen up to improve Premier League position
The Blues suffered their second successive away defeat when they fell to a 2-1 loss at Southampton. Following the game, Tuchel struggled to contain his anger towards his players, claiming it was too easy to score against them.
The German boss told BBC Sport:
"It is not enough to play 20-25 minutes on the level we want."
The Chelsea boss further added:
"It is too easy to put us off balance, to beat us, to confuse us," Tuchel told Match of the Day. "It is too easy. It happened against Leeds. We need to understand why and find solutions. We lose concentration, we lose our plan and lose consistency, it is too easy to beat us.
"You can always lose football matches and I am humble enough to admit this but in a match where you are in the lead there is no need to give away half chances. To have no answers in the second half was disappointing. We need to have answers, we need to step up and play a level higher if needed. We struggled to do this."
"Soft, soft, soft defending. There is no need to give shots away. Just toughen up as a team and show a different mentality."
Chelsea currently sit ninth in the Premier League table. They will next take on West Ham United at home on September 3.