The goalkeeper was sent off in stoppage time at Elland Road, where Rangers lost 1-0.
He was adjudged to have brought down Patrick Bamford, but it was subsequently established that no contact was made with the striker.
A successful appeal would mean Begovic would be available for Saturday’s home game against Blackburn rather than having to serve a ban.
Sam Field is suspended after picking up his fifth yellow card of the season in the Leeds game, while experienced duo Steve Cook and Jack Colback both went off injured and are doubts for this weekend.
Begovic was given his marching orders with the Whites leading 1-0 late on at Elland Road after racing out of his area to challenge Bamford, who went to ground. Replays suggested there was no contact and according to Ainsworth both players involved in the incident were agreed.
“Doesn’t touch him,” said the Rangers manager.
“I’ve had verification from both players there was no contact. Patrick is a great lad, he’s jumped out of the way and the referee thought he caught him. Hopefully we may be able to get one overturned, we’ll have to speak to the powers that be at QPR to see if we can appeal that. I’m gutted for Asmir, he’s been great for me this season.
Ainsworth saw his men dominated in the first half but they made a fight of it in the second with long balls pumped into the area in the later stages and could have levelled when a ball dropped around the penalty spot for Lyndon Dykes. The Scotland striker hooked goalwards but Leeds stopper Illan Meslier was there to produce a vital stop.
