Martial was United's top scorer with 23 goals last term but has only scored twice so far with both coming in the Champions League against RB Leipzig and Istanbul Basaksehir.
Solskjaer believes Martial's sending-off against Tottenham last month and a possible lack of confidence may be to blame for his problems.
"Anthony showed he made big strides last season, now it's time again to make even bigger strides and to develop more," said Solskjaer.
"He scored 23 goals last season, which was a big return. He took big strides towards becoming the striker he can be. Every season is a challenge and you cannot rest on your laurels at Man United. There are demands on every position.
"We want Anthony to kick on. for France against Portugal he showed his qualities as a centre-forward getting into positions but Rui Patricio made a few good saves and that might have affected Anthony's confidence.
"His conversion rate has always been good, but at the moment keepers have made good saves against him.'
"Anthony is no different from other players, he's not had a pre-season as normal and is getting ready for peak form.
"He had a three-game suspension, so he's lost too much football. But he scored against Basaksehir last time, good header, and I hope he'll get to his best again."