The Dutch legend is under increasing pressure at the Catalan giants following a stuttering start to the 2021-22 campaign, which hit a new low on Wednesday evening with a 3-0 defeat to Benfica in the Champions League.
Despite an unbeaten start to the La Liga season, three of the six matches have ended in draws, with dropped points against Granada and Cadiz fuelling speculation over the manager's future.
After losing Lionel Messi on a free transfer in the summer, and issues over registering new signings due to the devastating financial problems endured, Koeman's side are facing a testing transition period, but this has done little to ease the pressure on the former Netherlands manager.
According to the Daily Mail, Barca president Joan Laporta is an admirer of Pirlo, and has added him to a shortlist also containing Belgium boss Roberto Martinez and club legend Xavi, in case they decide to cut Koeman's time short.
The former AC Milan and Juventus midfielder has only one year of managerial experience under his belt so far - a disappointing campaign with the Old Lady in 2020-21, in which the Turin club only managed to achieve fourth place in Serie A on the final day of the season.
Financial restraints at Barca mean that Pirlo represents a cheaper option than the other two rumoured names, with Martinez and Xavi currently employed by Belgium and Al Sadd respectively.