The Croatian midfielder is again subject to rumours surrounding his future, with Spurs having missed out on Champions League qualification, which saw Harry Redknapp sacked as manager.
Modric produced a series of sterling showings last season and Ivanovic, whose side won the European Cup by beating Bayern Munich on penalties, believes the 26-year-old would be a valuable asset for Chelsea.
Will Modric be waving goodbye to Spurs this summer?
I don't know much about it other than what I read in the media, he told Sportske Novosti. I know there was interest in the transfer window before. Chelsea as a team have needed a player with these qualities. He would fit in quickly and strengthen the squad.
He has been in England a long time and knows about the way football is played on the island and the mentality of the players. He has exceptional quality, and moving to a bigger club is necessary for him to take the next step in his career.
I think at Chelsea he would adapt instantly and become a better player. He should come to Chelsea - it won't go wrong!
Eden Hazard and Marko Marin have both penned deals to move to Stamford Bridge in time for the new season, with FC Porto striker Hulk also likely to complete a move to the Premier League side.
Modric enjoyed a decent European Championship with Croatia, as Slaven Bilic's side crashed out at the group stage, after being defeated by Spain in their final group game.
The Spurs playmaker submitted a transfer request last summer and demanded a move to The Blues, with Tottenham having missed out on qualification for the Champions League.
However, he was denied a transfer to west London, and was forced to see out the season at White Hart Lane, where despite finishing in the top four, Spurs saw qualification for Europe's premier club competition evade them once again.
Manchester United have also been mentioned with a potential interest in Modric, but the addition of Shinji Kagawa might be the only addition to the club's midfield this summer.