No, it would be a violation of Indian sovereignty and a big indicator India is not going to be a major power. That is what countries do that cannot handle their own business.
I beg to disagree , nations throughout history have allowed allied militaries to utilize their facilities when faced with a common objective.This arrangement may be continued for as long as both nations deem it fit.
In fact even France hosted no less than 11 major American airbases in the period between 1950-67, these were
Bordeaux-Mérignac Air Base
Chambley-Bussières Air Base
Châteauroux-Déols Air Base
Chaumont-Semoutiers Air Base
Dreux-Louvilliers Air Base
Étain-Rouvres Air Base
Évreux-Fauville Air Base
Laon-Couvron Air Base
Paris-Orly Air Base
Phalsbourg-Bourscheid Air Base
Toul-Rosières Air Base
None of these meant that France had in any way capitulated to the Americans as senior or more powerful than them , it was simply a way of ensuring additional security until the french air force was strong enough to take on the soviets under it's own steam.
India is still growing towards becoming a world power and we share extensive interests with the yanks in preventing the PLAN from having a free run of the IOR and preventing piracy and ship borne weapons smuggling etc.
i believe we can an should host a small american flotilla at the mouth of the Malacca's just to irritate the Chinese for the time being