The Mail on Sunday says Allardyce has been offered several available strikers by agents in recent days.
So far the player on offer who has caught the eye of Allardyce most is former Newcastle United striker Martins.
The 29-year-old Nigeria forward has scored eight goals in 22 games for Seattle.
But given his Premier League experience, he could hit the ground running and would be an impact buy even if only on loan.
Allardyce has the benefit of having worked with the player when he was boss at Newcastle.
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball