The 22-year-old has been sidelined since undergoing an operation in July to address a long-standing left shoulder issue that had plagued him since 2023, forcing him to play through discomfort for both club and country.
"I want to be a bit optimistic and hope he can be back before October. He is starting to do some things with the group. He has made a great effort in his recovery. He is feeling very well," Alonso told a press conference on Friday as his side prepares to travel to face Real Sociedad on Saturday.
Bellingham, who joined Real Madrid from Borussia Dortmund two years ago, finally decided to go under the knife following the Club World Cup in the US after reaching his breaking point with the persistent injury. "I was sick of playing with the sling," he said back in June, having been frequently seen wearing shoulder strapping during matches.
The injury first flared up against Rayo Vallecano, forcing him to miss two games for both Real Madrid and England late in 2023.
His potential return would provide a massive boost to the LaLiga leaders, who sit top with nine points alongside Athletic Bilbao after winning all three opening games.
Fresh from a two-week international break, Alonso is pleased with his squad's condition as they prepare for a demanding period that includes their Champions League opener against Olympique de Marseille on Tuesday.
"The most important thing is that everyone has come back healthy, that we haven't had any injury problems," he said, setting his sights on maintaining their perfect start at the challenging Anoeta stadium.
“It will be demanding, every match is very important, both in LaLiga and in the Champions League, and these points could be decisive in the long run. We have to learn how to approach each match and focus on preparing well,” Alonso said.
“During these international breaks, we have to set short-term goals to get us through April and May. We don't want to lose focus. It's a way of talking about it and organising our thoughts by distributing goals and minutes."