Lambert, who has since managed Norwich, Aston Villa, Wolves and Stoke among others, has outlined why the 20-year-old should aim to extend his stay in Germany for years to come.
Sancho, who failed to hit the ground running at the start of the season, looked back to his best in their 3-0 victory over Club Brugge on Tuesday - setting up Erling Haaland and scoring a direct free-kick.
“I understand people saying that he’s a young kid and that he isn’t performing as well as he has been but now he is starting to really play,” Lambert exclusively told Daily Star Sport on behalf of BT Sport.
“I think the talk of Manchester United would unsettle him being a British guy, but he has got a special club in Borussia Dortmund.
“Once the fans come back, as he knows himself, there is no better place to play football because the atmosphere is incredible.
“Hopefully he helps the team to success.”
Lambert, who was praised for marking Zinedine Zidane out of the 1997 Champions League final as Dortmund won the competition for the first and only time, thinks this could be their season to shine.
He added: “I think this could be the year. With all the young guys like Haaland, Sancho, Giovanni Reyna and Jude Bellingham, alongside Marcos Reus, Mats Hummels, Thomas Meunier and Axel Witsel - they have top players.
“Hopefully this is the moment where they can overcome Bayern Munich, I think the club need a title whether it’s the Bundesliga or the Champions League or the DFB Cup.
“They have been so close in the last few years and hopefully, from an ex-Dortmund player, this is when they can get it. They’re going to have to overcome a really strong Bayern team.
“Everyone knows that they are really really strong, but hopefully this season in the year that they can get it.”
Dortmund sit one point behind leaders Bayern in the Bundesliga after eight matches of the new season, but they haven’t won the league title since back-to-back success under Jurgen Klopp in 2011 and 2012.
The Black and Yellows are looking good in the Champions League after the opening game defeat against Lazio, winning each of their following three matches to sit top of the group.
Up next for Lucien Favre’s side is the domestic tie against Cologne, who sit second bottom.
BT Sport is the exclusive home of the Bundesliga. Watch Borussia Dortmund v Cologne on BT Sport ESPN from 2.30pm on Saturday 28th November.