Boateng has been heavily tipped to leave the Bundesliga champions in recent weeks, with Manchester United said to have been interested before the window for signings for Premier League clubs closed on Thursday.
PSG are another team to have been linked with the 29-year-old, although Bayern head coach Niko Kovac has made it clear he would like him to stay.
Effenberg is bemused as to why Bayern would want to part with Boateng but has encouraged him to consider joining PSG as they represent a good chance for him to win the Champions League.
"Personally, I can't understand giving up such a great, experienced player. There can't be any sporting reasons," he told Bild am Sonntag.
"There was no commitment from the club for him. Despite his injury problems, for me, he's one of the best in the league.
"If I were his advisor, I would advise him to move to Paris, where he's welcome and would be able to win the Champions League."
Effenberg does not think Boateng's situation compares with that of Robert Lewandowski, however.
The striker's agent said in May that he wanted a new challenge and a move to Real Madrid was mooted, although it is looking increasingly likely Lewandowski will stay at the Allianz Arena.
Effenberg, though, thinks it is a risk to start the season with a player who openly wants to leave.
"If a player desperately wants to go, you have to let him," said the former Germany star.
"Taking a dissatisfied player into the new season is risky."