Earlier in the day, Comcast said it is in "advanced stages of preparing" a "superior" all-cash offer for the parts of Fox that Walt Disney has agreed to buy. However, Fox may find Comcast's bid less attractive since it would be taxable, versus a tax-free spin-off in a deal with Disney, sources told CNBC's David Faber.
Regardless, Hohn urged Murdoch in a letter, a copy of which was seen by CNBC, "to immediately engage" with Comcast. "The personal tax position of the Murdoch family must be an irrelevant consideration for the board, in order for the board to comply with their fiduciary duties," Hohn said.
Disney agreed in mid-December to acquire Fox's movie studios, the Nat Geo and FX networks, regional sports networks, stakes in Sky and Hulu and other parts of the company in a stock deal valued at about $66.1 billion.
Citing sources, CNBC reported earlier this month that Comcast was preparing to make a bid for the assets in mid-June. CNBC also reported that week that Comcast was preparing an all-cash bid of $60 billion, topping Disney's deal, if the government approved AT&T's acquisition of Time Warner.
Hohn added that he views the regulatory risk "to be equal and low" in the case of the Disney offer and any Comcast offer. He is also "confident" that AT&T will successfully win its bid for Time Warner.
Comcast, Disney and Fox declined to comment.
In a recent S-4 filing about the deal, Disney said the agreement with Fox prevents members of either party from engaging in any discussions about other proposals.
In a recent earnings call with analysts, Lachlan Murdoch, executive co-chairman of Fox, said, "We are committed to our agreement with Disney, and are working through the conditions to bring it to closing." He declined to comment on what he called "speculation" about Comcast.
Fox shares rose 1.9 percent in after-hours trading, while Disney and Comcast shares were unchanged.
Disclosure: Comcast is the owner of NBCUniversal, parent company of CNBC and CNBC.com.