The 21 year old is confident he will at least be back in time for a Christmas programme featuring games against West Brom, Crystal Palace and Bournemouth in the space of eight days.
"It's going really good. Better than I expected," Bellerin told the Daily Mirror. "It is a hard injury to recover from and a bit painful.
"But I am going to try to be running from this week and hopefully I'll be back on the pitch in less than four weeks."