Jimenez, who has only played four matches this season with Premier League side Wolverhampton Wanderers, was recovering from injuries to his knee and groin, but said his recovery has been slower than expected.
The 31-year-old fears he will not be ready for their World Cup Group C opener against Poland on Nov. 22 but is not losing hope.
"I am working with the ball, separated from the group, but I am already warming up with the team and I can do various things," Jimenez told ESPN Mexico.
"I'm not ready to compete yet. Physically I feel good, even though it's been (more than) two months since my last match.
"The squad list is due on Nov. 14. If I don't feel up to it by then, that's as far as it goes and I wish the team the best of luck."
The absence of Jimenez would leave Mexico without their two active top scorers, with Javier 'Chicharito' Hernandez not included in Martino's preliminary squad.
Should Jimenez miss out on selection, his place in Qatar could be filled by young Feyenoord striker Santiago Gimenez.
The 21-year-old is the joint top scorer in the Europa League this season with four goals. His winner against Lazio in a 1-0 victory on Thursday helped the Dutch side clinch a spot in the knockout stages.