A string of second tier clubs have been credited with an interest in the 23-year-old, though it is Rotherham who are said to have made the first move - offering £800,000 after having two previous bids rejected.
Omar Bogle scores for Grimsby
However, interest from Leeds and Norwich - both of whom have aspirations to become Premier League sides next season - could scupper the bottom club's chances of luring Bogle to the New York Stadium.
The pair are known to be in the market for new additions ahead of Tuesday's deadline, and a striker is thought to be among their top priorities.
Leeds boss Garry Monk is reportedly working on a deal for West Ham United striker Ashley Fletcher, though the deal may rely on the Hammers' capture of Brentford's Scott Hogan first.
West Ham United's Ashley Fletcher (right)
While Monk's Norwich counterpart Alex Neil is thought to have been chasing a new striker since the close of the summer window, with the Scot's current pool doing little to convince him otherwise in the meantime.
Bogle, who had never played in the Football League before Grimsby's promotion last year, has managed 19 goals in his first 26 League Two fixtures.
Would Bogle be a good signing for Leeds United/Norwich City?