The 23-year-old is out of contract in the summer and it is believed Town are looking to receive a fee rather than lose him for free later this year.
Striker Okenabirhie, Shrewsbury 16-goal top scorer last season, has found goals tougher to come by for Sam Ricketts' side this term.
He has managed two goals in 17 league appearances, six starts but has been omitted from Town's matchday squad for the last three games.
With Okenabirhie and fellow frontman Lenell John-Lewis, who is out of contract this week, set for exits, Ricketts is looking to boost his firepower this month.
Doncaster, up to eighth in League One after three wins on the spin, are also in the hunt for a striker this window and are understood to be in talks with Shrewsbury.
Town are looking to bring another centre-forward into Montgomery Waters Meadow but the boss does not believe his squad needs major changes this month.
Okenabirhie joined Town 18 months ago from National League Dagenham & Redbridge and found the net with regularity last season, leading to interest and an approach from league rivals Sunderland last January.
But the London-born former Arsenal youngster, who has 19 goals in 71 outings, looks to have made his last appearance for Town.
Ricketts said after Okenabirhie was again left out of the 1-1 home draw with Lincoln City: "It's just selection, I have to pick a team and can only have so many on the bench. That's the way that is."
Wigan loanee Callum Lang, who started for the first time in more than three months after coming back from a broken metatarsal, Jason Cummings and Daniel Udoh are Shrewsbury's other centre-forward options.