Fury beat American Kevin Johnson on points in Belfast on Saturday night, 24 hours after Price had knocked out Matt Skelton inside two rounds on Friday.
Fury's win puts him in line for a shot at the WBC title - either against incumbent Vitali Klitschko, or the winner of January's eliminator between Bermane Stiverne and Chris Arreola, if Klitschko decides to concentrate on his political career.
Price wasted no time in calling out Fury after his victory, and Fury's promoter Mick Hennessy says the deal can be done if both parties are serious about a showdown.
"What Tyson has said - and his entire team agrees - is that we would put a world title fight on hold for David Price if he stepped up to the table. If he's prepared to be sensible, we'll do a proper deal and this fight would happen," Hennessy said.
Eagles fly past Moycullen
BASKETBALL: Superleague leaders UL Eagles remain on top after an 88-72 victory over Moycullen with an admittedly 'scrappy' performance.
Elsewhere, Killester saw off UCC Demons 85-77. DCU Saints beat newcomers Dublin Inter (78-72) after the game went into over-time.
In Cork, Bord Gais Neptune outworked UCD Marian to record another win over the Dublin side (77-70). As Neptune's injuries begin to subside, the team are coming into form nicely.
In the women's competition, UL Huskies secured another win, beating Meteors 86-35, and sit comfortably on top of the table. In Cork, Team Montenotte Hotel beat WIT Wildcats 85-58.
Lynch second at Gucci GP
EQUESTRIAN: Denis Lynch won €60,000 after finishing second at the Gucci Masters Grand Prix in Paris. Riding Thomas Straumann's massive 12-year-old gelding Abbervail van het Dingeshof, the Tipperary man missed out on the €99,000 winner's purse by just 0.13 of a second in the seven-horse jump-off won by Dutchman Marc Houtzager on Tamino.
Kaymer on top in Sun City
GOLF: Martin Kaymer survived a late wobble to hold on for his first title of the year with victory at the Nedbank Golf Challenge in Sun City. The overnight leader bogeyed the 15th hole to see his advantage at the top of the leaderboard cut to one stroke by South Africa's Charl Schwartzel, but held his nerve the rest of the way to prevail by two strokes.
Kaymer finished on eight under par overall, with Schwartzel at six under and American Bill Haas alone in third, three strokes further back.
NFL: Chicago 17 Seattle 23 (OT), Green Bay 23 Minnesota 14, St Louis 16 San Francisco 13 (OT), NY Jets 7 Arizona 6, Kansas City 27 Carolina 21, Detroit 33 Indianapolis 35, Buffalo 34 Jacksonville 18, Miami 16 New England 23, Tennessee 10 Houston 24, Denver 31 Tampa Bay 13.