Chelsea had previously considered AC Milan's Mike Maignan, but were unable to come to an agreement on a transfer fee and have since withdrawn from the pursuit. Martinez, who is expected to leave Aston Villa this summer, is now being considered by the West London club.
At 32, Martinez is a experienced goalkeeper who has won the World Cup and has a strong track record in the Premier League. He has been heavily linked with a move to Manchester United, but Chelsea's interest is now a factor in his potential transfer.
Galatasaray, a Turkish football club, are also interested in signing Martinez as they look to replace their legendary goalkeeper Fernando Muslera.