"We have not yet decided whether to field candidate against Dimple or not," BSP leader Swami Prasad Maurya told reporters here.
When asked if there is any chance of BSP giving walkover to SP by not fielding candidate, he said it would be decided by his party's central leadership.
35-year-old Dimple, wife of Uttar Pradesh Chief Minister Akhilesh Yadav, today filed her nomination for the Lok Sabha by-election from Kannauj.
Reflecting the growing bonhomie between the two parties ahead of the presidential poll, Congress has decided not to field any candidate against Dimple, who had suffered a humiliating defeat at the hands of Congress' Raj Babbar in the by-election for Firozabad parliamentary seat in 2009.
The Kannauj by-election, to be held on June 24, has been necessitated following the resignation of Akhilesh after his election to the Legislative Council.