Comcast , which owns CNBC parent company NBCUniversal, has already publicly acknowledged its plans to compete with Disney on an acquisition of Fox assets, including Fox's movie studio, the Nat Geo and FX networks, regional sports channels, and stakes in Hulu, Star India and Sky PLC. CNBC reported last month that Comcast was preparing to raise $60 billion in a deal for Fox while simultaneously pursuing a $31 billion offer for the 61 percent of Sky that Fox doesn't already own.

Announcing an offer on Wednesday, rather than Tuesday afternoon, will allow Comcast's lawyers to look through the details of Leon's decision, the people said. Comcast advisors and executives believe Comcast's rival bid for Fox will put pressure on Disney's shares, as Disney may to have raise its outstanding $52 billion all-stock offer. Waiting until Wednesday, if Disney shares fall, could also accentuate the difference in value between Comcast's bid and Disney's offer, one of the people said.

Disney's hasn't said if it will improve its bid for Fox. A Comcast spokeswoman declined to comment.

Disclosure: Comcast, which owns NBCUniversal, parent company of CNBC and CNBC.com, is a co-owner of Hulu.