British satellite-TV provider Sky may be the last chance for Comcast’s Brian Roberts to get big in a hurry.

Comcast, which has been locked in a can-you-top-this contest with Disney for the prized Fox assets, is unlikely to submit a sweetened bid to top the leading $71 billion offer from the Mouse House, according to a report.

Instead, Comcast will turn its attention — and financial firepower — to its concurrent effort to win a bidding contest for Sky, CNBC reported, citing sources.

Comcast did not return calls for comment.

The cable-TV provider has been battling Fox for control of Sky. Fox owns 39 percent of the satellite-TV provider and is bidding for the remaining 61 percent.

Fox’s latest bid values Sky at $32.5 billion. Comcast’s latest bid valued the UK company at $34 billion.

“It looks like Brian is going to say ‘uncle’ ” on the Fox asset auction, one source said, pointing to a number of factors that include Washington’s regulatory approval of the Disney/Fox deal — as well as Fox Executive Chairman Rupert Murdoch’s expressed desire to partner with Disney.

Fox and News Corp., parent of The Post, have common ownership.

At the same time, Washington’s decision to appeal a recent court ruling that allowed AT&T to buy Time Warner may have spooked Comcast — convincing it to back away from pursuing Fox, one source said.

“If I’m Disney, I feel like I’m in the ring and I’ve bloodied my opponent,” BTIG analyst Rich Greenfield said of the Disney-Comcast battle over Fox and now Sky. “Comcast is falling down on the ropes and now [Disney] is going in for the kill.”

Comcast may sweeten its bid for the Fox assets but ultimately Disney will prevail, Greenfield said.

Media watchers said Comcast could buy smaller global assets like ITV or ProSieben — but neither would get it enough scale to compete internationally. Also, possible acquisition targets like MGM or Lionsgate wouldn’t give Comcast the heft to go toe-to-toe with Disney.