The Spanish international eventually completed a free transfer to the Camp Nou in September, after a prolonged departure from Premier League giants Chelsea, as Pierre-Emerick Aubameyang headed to Stamford Bridge.
The 31-year-old was targeted by Xavi to add experience to his back line as well as being able to cover at full back and in central defence.
Alonso initially signed a one year deal in Catalonia, but the club want to extend that beyond next season, after a solid start to life in Catalonia.
As per reports from Marca, FFP rules prevented Barcelona from offering Alonso a three year contact, as they initially wanted to, but their financial picture has since improved.
The report states Barcelona will open talks with Alonso’s representatives in January with a view to increasing his bond at the club until the end of the 2024/25 season.