The club, which this week signed left-back Matt Targett from Aston Villa, has an interest in Bayer Leverkusen winger Diaby.
And former Newcastle winger Waddle, speaking to BoyleSports EPL Betting, said: “Moussa Diaby would be my No.1 signing. He's quick and sharp, and has been linked with the club before.
"Newcastle have to convince players of a good standard to go to St James’s Park. They're on the up now, but they need to turn the corner and make the next step. It'll be very interesting to see who they bring in.”
United, however, could be priced out of a move for the 22-year-old Diaby, who wants Champions League football.
Saint-Maximin, linked with Tottenham Hotspur, has been a hugely-influential figure since joining United in the summer of 2019. However, Waddle feels that the 25-year-old – who scored five Premier League goals last season – can add more consistency to his game.
“Spurs are linked with Saint-Maximin, and their fans would be very excited to get him, but I think he'd be a very frustrating player for Antonio Conte,” said Waddle, who left Newcastle for Tottenham in 1985.
"He needs to be consistent, and provide more of an end product, if he wants to be a starter for Spurs every week.”