"We are not going to stake claim for the post of Vice President. We have no such intention," SP General Secretary Ram Gopal Yadav told reporters here.
He was asked whether SP plans to have its preferred candidate as the next Vice President in return for extending support to Mukherjee for the post of President.
The Vice-Presidential election is due in August.
To a poser, he also ruled out the possibility of SP joining the UPA-II government.
He said party supremo Mulayam Singh Yadav was present in Parliament House when Mukherjee filed his nomination as he was one of the proposers.