Liverpool in the International Champions Cup on Saturday.
"Man City and Tottenham are in the similar situation as we are".
He found the target nine times in Premier League competition last season, but was restricted to just 18 starts.
With Martial already absent from the squad, United boss Mourinho also confirmed both Antonio Valencia and Nemanja Matic will most likely be absent for the rest of the tour of the United States. Having impressed with Hull City and Leicester City in successive seasons, the player ended up becoming a vital cog for England at the 2018 FIFA World Cup.
"The first match of the season is against Leicester and the second one is against Brighton", Mourinho said.
"For me personally, I don't think I would want to sign a contract right now.", he said. "We had to wake up early because it was hitting 45 degrees by 10 o'clock - it was quite painful the first day as we did do it in that heat".
"So of course against Leicester and Brighton the situation is not wonderful for us. we will have to fight for the points with the players we have available".
Mourinho also said he did not know whether defender Marcos Rojo would be joining up with the squad in the U.S., having had "some physical problem". But, the player's ambition has grown after a stellar World Cup campaign.
Mourinho's comments to ESPN on Tuesday also included thoughts on Paul Pogba.
"To play for probably the best club in the world is a good thing, and for me, it's an honour to play here and play for Manchester United". Because it's closed for a month, where he can only think about football. He has just completed his own pre-season training camp in Dubai and has posted photos of himself on social media looking noticeably leaner.
"... maybe this season finally you demand that they win".