United manager Alex Ferguson said last week Rooney was likely to be sidelined for up to three weeks with minor ankle ligament damage sustained in their 2-1 first leg defeat.
But he told ITV Sport before kick-off: "It was not a serious injury but obviously he wasn't fit for Saturday but the progress in the last two days has been incredible.
"Yesterday afternoon, he did some real good training. I made my mind up after I saw him training yesterday. He's not done a lot of training but we hope the work he's done in the gymnasium compensates.
"There's no risk as it was a soft tissue injury, not ligament damage. He can play without worry of a recurrence. I hope he makes an impact."
Rooney was injured in the dying seconds of last week's match in a challenge with Mario Gomez and he left the Allianz Arena on crutches and with his foot in a protective plastic boot.
He did not take part in an open training session on Tuesday and Ferguson gave every indication he would not risk the player unless he believed he was 100 percent fit.
Rooney, whose goal in Munich last week was his 34th of the season, missed Saturday's home defeat against Chelsea.
His injury caused widespread concern in England, with even British Prime Minister Gordon Brown referring to it, because Rooney's fitness is seen as vital to England having a successful World Cup in South Africa.
Manchester United: Van der Sar, Rafael, Vidic, Ferdinand, Evra, Valencia, Fletcher, Carrick, Gibson, Nani, Rooney.
Subs: Kuszczak, Evans, O'Shea, Scholes, Giggs, Berbatov, Macheda.
Bayern Munich:Butt, Lahm, Van Buyten, Demichelis, Badstuber, Schweinsteiger, Van Bommel, Ribery, Robben, Muller, Olic.
Subs:Rensing, Altintop, Klose, Pranjic, Contento, Gomez, Tymoshchuk.
