Coquelin was injured in the 2-1 Premier League defeat by West Brom on Saturday, but midfielder Ramsey's comeback could bolster a depleted Arsenal side as they strive to keep their Champions League knockout phase hopes alive.
The Gunners are level on three points with Zagreb and trail Bayern Munich and Olympiakos Piraeus by six points in Group F after four of six matches.
"Certainly for the next two months we play without Coquelin. I'm cautious as we had so many bad surprises on scans that I do not want to speculate more than that," Wenger who has "not completely decided" whether to risk Ramsey for the first time since the Oct. 20 win against Bayern Munich, told reporters on Monday.
None of Theo Walcott, Alex Oxlade-Chamberlain, Jack Wilshere, Danny Welbeck, Tomas Rosicky or Ramsey were available at the weekend, while Coquelin's replacement Mikel Arteta came off after 35 minutes with a calf strain.
"We've been hit very hard in November because until the Sheffield Wednesday game in the League Cup we had a good record but since have lost a few players," added Wenger.
"We have Ramsey and maybe Oxlade-Chamberlain back for the weekend and Walcott will be the next one -- all the other players are long-term injuries."
Arsenal, who lost 2-1 to Zagreb in the opening match of the Champions League campaign in September, need to win and hope Olympiakos lose to have a chance of overhauling them for second in the group. Wenger's side cannot overtake Bayern.
Wenger also backed under-pressure Real Madrid boss Rafa Benitez after his side suffered a humiliating 4-0 defeat by arch-rivals Barcelona in the 'Clasico' at the weekend.
"I would just like to take this opportunity to support completely Rafa, who is an outstanding manager and it would not be serious to sack the manager after 12 games," said Wenger.
"I hope he gets support of the president. No one should bet on me to become next manager."
(Reporting by Rob Hodgetts; editing by Justin Palmer)
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