Bresnan was forced to pull out of England's recent tour of New Zealand after having surgery to repair a persistent elbow problem.
The 28-year-old has declared that his rehabilitation has gone well and should allow him to take part in Yorkshire's three-day friendly with Lancashire, which begins on Tuesday, April 16.
He told Sky Sports News: "[I'll be back in] a couple of weeks I think, all being well. We've got a three day friendly against Lancashire so I'm targeting that game, I should be able to play a full part in it.
"It's coming back strong now. I'm back bowling in the nets against the lads so I'm looking forward to getting out there and playing some cricket. It's always frustrating being injured. You've just got to take it on the chin, its part and parcel of the game.
"You are going to get injured at some point, hopefully not that often and hopefully not that severe but the way international cricket is these days, you play so much of it, it's inevitable really. I can't wait to get going now, the elbow's feeling a lot better than it was before the operation, even though I'm not fully fit yet."
Bresnan is fighting for a place in Alastair Cook's squad for the return Test series against New Zealand next month ahead of back-to-back Ashes campaigns.