Speaking at the UEFA Congress in Belgrade, Infantino said the only bid for 2031 was "from the USA and potentially some other CONCACAF members together, and 2035 is from Europe, from the home nations".
Infantino also said FIFA planned to increase the number of participating teams at the Women's World Cup from 32 teams to 48 in time for the 2031 tournament.
Thursday's announcement comes after the football associations of England, Scotland, Wales and Northern Ireland revealed last month that they would submit an expression of interest in staging the tournament.
World football's governing body last month said it would only welcome bids for 2035 from Europe or Africa, saying that the identity of the hosts would be confirmed at a FIFA Congress in the second quarter of 2026.
The United States - who are co-hosting with Mexico and Canada the 2026 men's World Cup - also confirmed in early March that it would push ahead with a bid for 2031.
South Africa and Morocco had also been in the running with African nations invited to bid too, but Infantino's comments suggest they are now out of the running.
The next Women's World Cup will take place in Brazil in 2027.
