Concerns over error-prone De Gea, 29, and a reluctance to make Henderson, 23, first-choice means United are keeping tabs on Meret, 23, according to ESPN.
The report claims Ole Gunnar Solskjaer still sees De Gea as his No 1 at Old Trafford.
Manchester United could move for Napoli goalkeeper Alex Meret this summer
That would see Henderson sent out on loan again with Sheffield United keen to extend his stay at Bramall Lane.
Sergio Romero will continue his long spell as United’s experienced back-up.
And Meret is the man Solskjaer will turn to if any of those three choose to leave.
The Italian has been capped at every international level from under-16 to full senior star. Meret made his debut in Italy in November last year, coming off the bench in the 9-1 Euro 2020 qualifying win over Armenia.
Ole Gunnar Solskjaer still sees error-prone David de Gea as his No 1 at Old Trafford
Dean Henderson (above) could face the prospect of going out on loan again next season