The Cottagers are currently battling to keep hold of Joao Palhinha, who has made it clear that he wants to join Bayern Munich.
The Bavarians are pushing to complete a deal and Fulham would need to bring in a replacement if Palhinha departs.
They are looking at options and have now made contact with Manchester United to discuss McTominay.
He is seen by Fulham as someone who could come in and replace Palhinha late in the transfer window.
Fulham though face needing to fork out a substantial sum to convince Manchester United to consider letting McTominay go.
The Red Devils are currently trying to bring in another midfielder.
They are chasing the services of Fiorentina star Sofyan Amrabat and are trying to convince La Viola to let him leave for England on loan.
