Martial has made a blistering start to life at Old Trafford since his £36m move from Monaco on deadline day.
Meanwhile, Memphis grabbed his first Premier League goal against Sunderland at Old Trafford last weekend.
Schweinsteiger believes the pair will “give a lot of power” to Man United in the coming years.
“Yes, they can achieve a lot,” Schweinsteiger said when asked about Martial and Memphis.
“They are both very young but both very talented. If they make the right decisions and take the right steps in the future, then they can give a lot of power to Manchester United. For me, the most important thing is that they have a good personality and a good character, and they do! That is what’s most important, and with the quality they can achieve a lot.
“I will try to guide them, of course. I have played a lot of matches at that level and it is always a little bit different to Premier League and Bundesliga games.
“It is always a special night when you walk onto the field and the anthem comes on. It is a big honour to play Champions League games, so I will try to give my best and try to help my younger team-mates.”
Schweinsteiger is a born leader and there aren’t many better players to have when it comes to guiding young players in the squad. It will be a while until supporters see the best of Martial and Memphis but they have certainly got off to excellent starts considering the furore surrounding both of their arrivals.