Aston Villa are working to move Martinez on before Tuesday's deadline, with the goalkeeper offered to Chelsea after his proposed transfer to Juventus collapsed earlier this month despite the Italian club's initial £6m offer.
Zion Suzuki's arrival at Villa Park has left Martinez as one of three senior goalkeepers on Unai Emery's books, with the Spaniard intending to press ahead with Suzuki and Marco Bizot as his first-choice pairing regardless of what happens with the Argentine.
Martinez is also Villa's highest earner following Youri Tielemans's departure to Manchester United in July, adding financial pressure to a squad that cannot realistically carry three goalkeepers on senior wages. The 33-year-old has continued training with Villa since returning from the World Cup and the club say he is not injured, but a permanent exit is now the preferred outcome for all parties.
At Chelsea, the timing has coincided with fresh scrutiny of Robert Sánchez's form after a shaky display in the club's 3-2 win at Fulham.
Manager Xabi Alonso had earlier in the summer said he was happy with his goalkeeping options, which also include Mike Penders, the 21-year-old Belgian signed after a successful loan at Strasbourg. Discussing Sánchez this week, Alonso downplayed any individual concern.
"Normal conversations. We have talked more about the team thing, about what we did well and what we have to do better. It was more about understanding the context," he said.
"Every game is going to be important because we are in this process that we still need to develop things, we need to make adjustments that are more team-related."
Penders, likened by some at the club to former Chelsea goalkeeper Thibaut Courtois, looks set for a rare start on Thursday in the Carabao Cup against Luton Town.
"He's in the squad and will have an opportunity," Alonso said. A move for Martinez, at 33, would not be viewed internally as a block on the young Belgian's progress given the difference in career stage between the two goalkeepers.
Villa have also sent a forward out on loan this week. Tommi O'Reilly has joined Doncaster Rovers for the season, returning to League Two after playing every fixture there last season during a loan at Crewe Alexandra.
The 22-year-old, who has also had loan spells at Shrewsbury Town and MK Dons, said he was looking forward to the new challenge.