And the Argentina winger has recently turned down a big money move to the UAE, leaving his situation uncertain.
A 24.6million release clause means he would be more expensive than Pedro.
Nicolas Gaitan - Spotlight On
Invalid email
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy
That has been followed up by today's reports in Germany which suggest an €85m (£60m) bid has been made by United.
Muller would be seen as a game-changer for Van Gaal, who worked with him during his time in Germany.
And while Bayern are notoriously difficult to buy from United have already signed Bastian Schweinsteiger this summer.
Thomas Muller - Spotlight On
Edinson Cavani
The Uruguay striker would offer United an option in a more central role, however he has been used out wide at PSG to accommodate Zlatan Ibrahimovic.
United currently look light through the centre with just Wayne Rooney, Javier Hernandez and youngster James Wilson.
But the move for Pedro hints that they are happy to go with that and would prefer another winger to compliment Memphis Depay, Ashley Young, Juan Mata and Adnan Januzaj.
Edinson Cavani - Spotlight On
Gonzalo Higuain
Another who would offer more through the middle, Higuain is keen to leave Napoli if they can find a buyer.
However the Serie A side are holding out for a staggering £66.8million.
The former Real Madrid man came close to joining Arsenal before securing his switch to Napoli but with them failing to qualify for this year's Champions League he wants to move on.
Gonzalo Higuain - Spotlight on
Juan Cuadrado
The Colombia winger was on United's shortlist after an impressive World Cup, but eventually moved to Chelsea.
His move to the Bridge hasn't worked out and Chelsea are happy for him to leave.
And while a move would be controversial Chelsea have sold Mata to United and Petr Cech to Arsenal, so not totally out of the question.