Shares in Juventus, Italy's most successful football club, rose as much as 4.8% at the opening but quickly trimmed those gains to be up just 0.3% by 10:00 BST, broadly in line with the Milan bourse as a whole.
A spokesman for Exor said in a statement that Il Giornale's report was "groundless" after the newspaper reported that the holding company considered Juventus's recent financial results were "no longer sustainable" and it had been embarrassed by the football club's ongoing judicial problems.
Juventus, its former Chairman Andrea Agnelli and 11 others could face trial after judges in Italy last year launched a criminal case against them over allegations of false accounting.
The club has denied wrongdoing and said its accounting is in line with industry standards.
Reuters reported in May that representatives of the Agnellis had become more open to ideas about the financial future of the club, citing five people in regular talks with them.
Exor said then its commitment to Juventus was unchanged and that any suggestion to the contrary was totally without foundation, was misleading and intended only to create uncertainty.
The people added to Reuters that no imminent changes were expected and that any possible decision would only come once there was clarity on the accounting and judicial clouds hanging over the club.
Exor owns around 64% of the shares and 78% of the voting rights in Juventus, which has a market value of around 800 million euros, according to Refinitiv data.
According to Il Giornale, Exor believes it could put Juventus up for sale for at least 1.5 billion euros (£1.29 bn), after taking measures to resolve its accounting issues.
The investigation into Juventus's accounts also triggered separate inquiries by Italy's soccer authorities which eventually cost Juventus a 10-point deduction in the past Serie A season, a 718,000 euro fine and a ban, decided by UEFA, from this season's European competitions.
Juventus has absorbed some 700 million euros in cash from shareholders over the past four years, roughly two-thirds of which has come from Exor, in whose portfolio the club is the only major business not currently making money.
