BSP national General Secretary Satish Chandra Mishra confirmed that his party chief had given an application for withdrawal of the case in the Supreme Court but did not give any details.
Samajwadi Party's chief spokesperson, Rajendra Chaudhary, said, "I am not aware of it yet. Will find out about it and then only say anything on it."
Another BSP leader said the case was still pending in the Supreme Court.
According to sources, Mayawati said in a meeting of party workers on Thursday that Akhilesh Yadav had requested her to withdraw the 24-year-old case against his father in the run-up to the Lok Sabha polls.
She said she had asked party's Rajya Sabha MP Satish Mishra to look into the matter.
The State Guest House incident took place on June 2, 1995 when the SP-BSP coalition government was in power in Uttar Pradesh.
Mayawati was addressing meeting of BSP MLAS over the issue of continuing support to the then Mulayam Singh government.
Samajwadi leaders attacked the State Guest House and Mayawati and the BSP MLAs locked themselves in a room to escape their wrath.
Several hours later, she was rescued by BJP leaders and then went on to become Chief Minister with support from the BJP, following the dismissal of the then Mulayam Singh government.
A case was registered at a Lucknow police station in which Mayawati claimed that the incident was designed to kill her. Several prominent SP leaders of that time were also named as accused in the case.
The incident changed political equations in Uttar Pradesh and SP and BSP became sworn enemies till 2019, when Akhilesh Yadav struck an alliance with Mayawati, who later clarified that Akhilesh Yadav was not in politics when the 1995 incident had taken place.
The alliance, however, did not last and soon after the Lok Sabha elections, Mayawati called off the alliance with SP.
( With inputs from IANS )