The Arsenal midfielder has been struggling with an ankle injury that has seen him miss his club's last two matches, against Liverpool and Borussia Dortmund, with Arsene Wenger hinting that he would not be available for international duty.
However, after liaising with doctors from both club and country, Hodgson is optimistic that the 21-year-old can play a part in at least one of the games.
"We're in constant discussions with Arsenal," he told reporters. "Gary Lewin and Ian Beasley are always talking to their medical staff.
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"With any luck he'll be fit at the weekend and he'll play in the game and there'll be no further things to discuss. If that wasn't the case then I think it will be a question on a day-to-day basis."
Wilshere's recent ankle problem is reminiscent of the injury that saw him spend 14 months on the sidelines and miss the entire the 2011-12 season but Hodgson insists that the current issue is unrelated.
"It'll be a question of discussing how much better is the ankle now because it's nothing to do, from what I understand, with his previous ankle problems," he continued. "This was a kick on the ankle which caused it to swell up and the inflammation needs to die down.
"With Jack I think it will be a question of our medical staff and Arsene and I constantly discussing it. Arsene, as far as I can make out, is not averse to him playing in at least one of the games; it's a question of whether or not it's going to be fit enough to play in one of the two games."