The north London side are reported to be leading the race for the South American after Liverpool had initially appeared to be favourites to sign the playmaker this summer.
The 25-year-old, who scored 37 goals in 222 games for Shakhtar Donetsk before joining Anzhi in January, has previously spoken of his desire to move to the Premier League.
And former Anzhi and Manchester United coach Meulensteen heaped praise on Willian.
“I’ve worked with him for a short time but I really, really like him. He will be an asset for whoever’s going to get him,” said Meulensteen on Sky Sports News.
“If it’s Spurs that’s going to get him they’ll get an excellent player. He’s very versatile, he can play in different positions, he’s a very creative player and an excellent professional with a very good personality.
“He’s going to be a major trump card for Spurs if they can get the deal to go through.
“He can beat a player, he can score a goal. I thought he was an absolute delight to work with.”