Thuram can operate as a forward or left winger and has also been linked with a transfer to Manchester United.
The 25-year-old has been in fine form in Germany this season, scoring 13 goals across 17 appearances for Bundesliga club Borussia Monchengladbach.
Thuram has entered the final six months of his contract at Gladbach and is thought to be available for as little as €12m (£10.5m) when theJanuary transfer window reopens.
But Saint-Maximin is hoping Thuram will snub both Liverpool and United to join Newcastle instead.
Eddie Howe’s side – currently third in the Premier League after a strong start to the season – were taken over by a Saudi-backed consortium in October 2021 and now have the money to compete with the traditional ‘big six’ clubs.
‘He is a great player and I hope we have a chance to take him here [to Newcastle],’ Saint-Maximin told The Gazette about Thuram.
‘I was so happy for him [to play at the World Cup]. Yeah, I will be honest, I have chatted with him.
‘For me, he’s a great player. I’ve known this guy a long time. I’ve been playing football with him when I was very young.
‘I know all his family. He has great parents. He’s an incredible guy.’
‘Marcus Thuram and Randal Kolo Muani made a brilliant contribution [in the World Cup final against Argentina] in very difficult circumstances,’ Saha told Paddy Power.
‘They maintained their composure in crucial moments, and they are great players.
‘At this moment in time, young players moving to Manchester United need to be cautious because we have seen some really good players struggle at United.
‘I’m not saying they shouldn’t join because of that, but it’s a difficult time.’