Arsene Wenger is hopeful of having the England international available to face Liverpool on February 8, but is expecting the Welshman to be out for "some weeks" with a thigh injury
Goal revealed Wilshere was struggling with the injury prior to the trip to Southampton on Tuesday, with the England international missing the 2-2 draw, while Ramsey is set to be out for up to six weeks.
But Arsene Wenger is hopeful Wilshere will be fit to face Liverpool at Anfield on February 8.
"We have good news," Wenger told reporters. "For Sunday he will be short but he has a chance to be available for the week after at Liverpool."
Aaron Ramsey, meanwhile, remains out after suffering a setback in his recovery from a thigh problem.
"Ramsey will be out for longer because he had a setback and it doesn't look too good," Wenger added. "It is matter of some weeks for him."
Injuries to the pair have forced Arsenal into the transfer market late in the January window, with Wenger targeting a midfielder.
The Gunners have contacted Paris Saint-Germain over the possibility of signing Blaise Matuidi, Goal understands.