The former Germany international backs the Dutchman to make a winning return to the Bavarians and credits Lucien Favre with reinvigorating Monchengladbach
The Dutchman has been criticised in recent times for being too selfish, but he has received the backing of Effenberg, who also believes the Bavarians will be pushed all the way by Borussia Monchengladbach in the title race.
After an incredible escape from relegation last season, Lucien Favre's side have established themselves at the right end of the table, and Effenberg feels they are capable of challenging Borussia Dortmund and Bayern at the top.
"Bayern are my favourites but Gladbach have no reason to hide. They play football that is deserving of the title of 'champion'," Effenberg told Bild.
"The 1-0 victory in Munich on matchday one opened the door. But no one may speak of a streak anymore."
"Bayern are well advised to remain calm. Without Robben, it is difficult to win a title. Bayern need Robben - no ifs or buts."
Effenberg, who enjoyed two stints at Gladbach and Bayern as a player, credited Lucien Favre with masterminding the turn-around at Borussia Park.
"This is an unbelievable and great story. Lucien Favre has managed to make the players support him unconditionally.
"This is due to the painstaking work of Favre. He has strengthened the defence. Last season, Gladbach were the shooting gallery of the league, now they have the best defence. Favre is able to push all his players to the limit."
Monchengladbach sit one point behind Bayern in the Bundesliga table, with both teams looking to displace Dortmund who are two points clear.