McStay has become a strong favourite to replace the already departed James Horan, who left after another disappointing campaign for Mayo.
Mayo were well beaten by Kerry in this year's Championship and with that Horan decided to walk away from the role.
Horan held the reins in the county for eight years across two stints.
McStay, a former Roscommon boss has reportedly put his name forward to take the job fulltime ahead of new season.
Kevin McStay puts name forward to become Mayo manager – and assembles star-studded backroom team https://t.co/xODOpzrrP8 pic.twitter.com/HgktDQP0ni — Independent Sport (@IndoSport) July 28, 2022
According to a report from RTE Sport the deadline for nominations for the post will close on Friday evening.
The two-time Connacht medal winner is also rumoured to have assembled a strong backroom team that includes the likes of Stephen Rochford, the former-Mayo manager and Donegal coach, former Mayo player Liam McHale, All-Ireland winner with Cross Molina Damien Mulligan and Donie Buckley.
When the deadline has passed, candidates will be assessed before interviews are held.
It is expected that the new manager will be in place before club championships start