With Pierre Gasly moving to Red Bull Racing, the energy drink company is looking for a replacement but is so far unable to secure a super license for preferred successor Dan Ticktum.
Last week, rumours emerged that former Red Bull and Toro Rosso driver turned Ferrari development driver Kvyat was back in the running.
“At this point in the season there are always a lot of rumours, and that is especially true in Monza,” said Red Bull team boss Christian Horner.
As for the Kvyat rumour specifically, he is quoted by Speed Week: “I think the situation at Toro Rosso is very open, so all sorts of options are being considered.
“Daniil is one of several drivers eligible for a Toro Rosso seat next year,” he added.