The France international is vying to start in a centre-forward role in the Manchester United team following Romelu Lukaku’s move to Serie A giants Inter Milan.
Alexis Sanchez has also been linked with a move to Inter following the Chile international’s well-documented struggles at the 20-time English champions.
Rashford scored twice in Manchester United’s 4-0 victory over Chelsea FC at Old Trafford in their season opener in the Premier League.
Martial got on the score-sheet against Chelsea FC before the France striker found the net in a 1-1 draw with Wolves on Monday night heading into this weekend’s clash with Crystal Palace.
The former AS Monaco forward has been used on the left wing throughout most of his Manchester United career apart from his first season under Louis van Gaal.
However, Martial was quick to rubbish any suggestion of a rivalry between the Frenchman and Rashford to secure a starting spot as Manchester United’s centre-forward.
“At training, we have this competition between us about scoring goals,” Martial told Sky Sports.
“We measure who does the best finishing and who scores the most.
“Who’s winning? Well, that depends… Sometimes it’s him, sometimes it’s me. In games, Marcus likes to play in the middle, like me.
“I don’t mind dropping off, dropping out, we interchange during games.
“It doesn’t bother me to let him take the lead occasionally. It helps us to terrorise opposition defences and I hope we can keep it up over the course of the season.”
Martial moved to Manchester United in a £36m deal from Ligue 1 side AS Monaco in the 2015 summer transfer window.
The France international’s goal against Wolves was his 50th since moving to Manchester United four years ago.
The Red Devils will return to Premier League action with a trip to Southampton on Saturday lunchtime next weekend.
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