Messi has been linked with a shock move away from Camp Nou after supposedly being left upset by a number of off-the-field issues over the past 12 months.
The Argentina international is due to become a free agent at the end of next season and, according to certain reports, Inter and Juventus are in the running to sign the forward.
In the same way that Italian carmakers Fiat played a big part in Cristiano Ronaldo's move to Juve in 2018, Pirelli may now chip in to bring Messi to San Siro.
However, Tronchetti also acknowledged that the coronavirus pandemic will make it even more difficult to complete a deal.
"Honestly, at a time like this, we're unable to invest in sports more than we are, between Formula 1, the America's Cup and Inter," he is quoted as saying by The Mirror.
"We have to ask [Inter chairman] Steven Zhang to make an effort himself. We can help, but we can't do anything significant."