According to Javier G. Matallanas of Madrid-based newspaper AS, both have keen interest in the 27-year-old. The Premier League transfer window already shut on Aug. 9, but the report noted he could be available for as little as €30 million.
Such a valuation would be remarkably low, as Alonso is a key starter for the Blues―something the report acknowledges. Add to that the fact that Chelsea can no longer bring in a replacement, and a transfer seems virtually impossible this summer, especially for such a minimal fee.
Football writer Paul Brown didn't think a move is likely:
Matallanas added both clubs could still battle it out for his services in the future if he doesn't leave the Premier League this summer.
Alonso was on the books at Real once before leaving for Bolton Wanderers in 2010, and via Italian side Fiorentina, he ended up at Chelsea. He's been an excellent producer for the Blues and bagged the winner against Arsenal during the weekend.
Atletico in particular could be in the market for another left-back if Filipe Luis ends up leaving for Paris Saint-Germain. Per the report, a move for Alonso would be contingent on a Luis deal.
Real sent Theo Hernandez on loan to Real Sociedad and have limited depth at the left-back position, but in Marcelo, they have arguably the best starter in the game right now. Alonso is not likely to leave Chelsea for a spot on Los Blancos' bench, even if it would mean a return to his place of birth.
With plenty of time left on his contract, Chelsea hold all the cards, so unless one of the La Liga giants are willing to pay big money, he likely won't be going anywhere.