Most top universities are unlikely to set up an Indian campus -- the list of universities that have said 'no' to this option is pretty long: Yale, Columbia, Brown, Oxford, Cambridge, ...
Here, for example, is Prof. Andrew Hamilton, Vice Chancellor of Oxford:
We have many links to India already but we have no plans...in the foreseeable future to establish a campus in India and we have no plans to offer degree courses anywhere other than Oxford for the time being.
Any particular reason?
Oh, I think there are many reasons. Oxford is an institution 800 years in the making and recreating the very special environment that sits in 700-year-old colleges and the living environment that they provide and that critical mass of scholars and students that is present in Oxford, that is a very hard thing to reproduce anywhere else.
Would it be accurate then to say 'Oxford' is not really a brand you're interested in franchising?
Universities are much more complex than talking of hamburgers and franchises.
[The last answer is brilliant, isn't it?]
I think we now have some clarity on the most likely option for foreign universities that wish to have a presence in India.
Partnerships and Collaboration.
This option offers a lot of flexibility, and could take many forms -- short term exchange programs (study tours and semester-long stays), summer internships, and / or longer programs where students do their coursework in India and do their final year projects overseas.
The Indian partner can advertise the tie-up with foreign universities; the foreign partner will have a dependable host in India to send its students to under an exchange program. The overseas partner may also manage to extract some 'earnest money' from the Indian partner -- all of which will end up increase the cost of education in these colleges and universities.
There's also a potential upside: If the partnership is broad enough to include faculty exchanges (and long term collaborative research), it will be a huge plus for India -- India will benefit from the expertise of people who have worked under many different kinds of environments.