City captain Gundogan is entering the final three months of a four-year deal he signed back in 2019, and the Germany international is yet to agree to fresh terms.
Gundogan has appeared in 24 of City's 27 Premier League games this campaign, yet reports have claimed he has his heart set on a move to Camp Nou at the end of the season.
Despite suggestions Barcelona are willing to offer Gundogan a two-year deal, the player's agent and uncle Ilhan Gundogan says nothing has been decided.
"There's definitely no agreement yet with any club," he told The Guardian. "The focus of Ilkay in recent weeks was only on Manchester City and the birth of his son.
"Now he is in the final and crucial phase of the season and is completely focused on that. Where Ilkay plays next season is still open."
Gundogan has won four Premier League titles since joining City from Borussia Dortmund in 2016, scoring twice in a comeback win over Aston Villa to hand Pep Guardiola's team their latest triumph on the final day of last season.
The 32-year-old did not feature for Germany in the recent international break, with Hansi Flick opting against calling him up after the birth of his child.