English publication the 'Daily Mail', reports that the 34-year-old is one of a number of names on Barca's list of targets as they look for cover for the injured Samuel Umtiti.
Umtiti is currently sidelined with a knee injury and with Thomas Vermaelen also suffering intermittent injuries and Yerry Mina having joined Everton during the summer, there is a concern that the Spanish champions are short on numbers at the back.
Ivanovic is out of contract at the end of the season, though his current employers have the option to extend his stay by a further year.
The experienced defender is best known for his nine-year spell with Chelsea, making almost 400 appearances for the Premier League side.
The difficulty of doing business in January means that Barca are considering players that are in precarious contract situations or who are out of favour at their current side as they look to make some short-term improvements to their side at the turn of the year.
Crystal Palace and Fulham are both thought to have registered a tentative interest in Ivanovic's services as they look to add Premier League experience to their squads, but a move to the Camp Nou is likely to prove difficult to turn down for the Serbia international.