United confirmed on Thursday that the France global has agreed a new contract to keep him at the club until 2024, while they have the option to extend it by another season.
Solskjaer has reinvigorated the France forward's United career since replacing José Mourinho as manager in December.
Martial has scored eight goals in 18 league matches this season.
"And they should still continue to do that, because you don't know what's going to happen in the next three or four months".
"Cristiano was the best, the way he's changed to now, that's the player you've got to model yourself on and you've got to have more challenges ahead of you".
However, with miserable Mourinho gone, Martial has been given license to express himself under new caretaker-boss Ole Gunnar Solskjaer, who has made him one of his first choice forwards at the club alongside Marcus Rashford, with the Frenchman putting pen to paper on a new long-term deal earlier this week.
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Solskjaer played in the same Man Utd team as Teddy Sheringham, Andy Cole and Dwight Yorke and is looking to improve Martial's instincts in and around the box.
Speaking about the deal, former Manchester United midfield maestro Paul Scholes couldn't contain his delight that Martial will be staying at the club until 2024. "I made my career here, it was easy to sell the club to Anthony but he's been here for many years so he knows what we're capable of".
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The France worldwide joined United back in 2015 from AS Monaco for a £36m ($47m) fee and he has since enhanced his reputation as one of the best young players in European football. Anthony has done some rehab work, so he will try a session today. "I certainly believe in him".
"He's got fantastic potential", added the Norwegian.
"He's had some ups and downs at the club, he's been top scorer, he's been developing", said Solskjaer.