"Things are going really well at the moment," he said, per Sky Sports. "We're really happy to have him here with us. I hope we can continue with him as our head coach, but ultimately the final decision isn't down to us. But we're pleased he's with us at the moment."
The Norwegian replaced Jose Mourinho in the Old Trafford hotseat in December.
He has overseen a turnaround in form at the club, winning 10 of his 11 games in charge so far. United were in sixth place in the Premier League when he arrived but moved into the top four with victory over Fulham on Saturday:
Martial also explained the difference in approach between Solskjaer and former manager Mourinho:
Solskjaer has brought an attacking approach to Manchester United's play that has seen players such as Paul Pogba and Marcus Rashford thrive:
12 - Paul Pogba and Marcus Rashford have combined to create 12 scoring chances for each other in nine competitive games under Ole Gunnar Solskjaer (692 mins). They only combined for five scoring chances in 17 matches under Jose Mourinho in 2018-19 (814 mins). Wavelength. https://t.co/L3auTbZuC9
Martial has also been influential this season for the Red Devils, with nine goals and two assists in the Premier League.
The 23-year-old committed his future to the club in January by signing a new contract until 2024, with the option to extend it for another year, per the club's official website.
Solskjaer has said Martial has the potential to reach the same level as former Manchester United star Cristiano Ronaldo, per BBC Sport.
"If he wants to be at Cristiano's level, Anthony knows what he has to do," he said. "It's up to him. He has the talent."
Solskjaer has Manchester United moving in the right direction after a frustrating time under Mourinho. He clearly has Martial's backing, and it would be little surprise if he were named the club's next permanent manager.