Chelsea had agreed with Fernandez's agent, Javier Pastore, in late May that the Argentina midfielder could leave for £120m, and set a deadline of 14 August for any bids to be submitted.
That deadline passed without a formal offer materialising, and Chelsea have since told Fernandez's camp that he is not for sale for the remainder of the window.
Manchester City, managed by Fernandez's former Chelsea boss Enzo Maresca, are keen to sign the 25-year-old and believe the London club still want to do business, but Alonso indicated on Thursday that the player's focus is firmly on Chelsea's Premier League opener at Fulham on Monday.
Asked in his pre-match press conference whether Fernandez would still be at Stamford Bridge when the transfer window shuts on 1 September, Alonso gave a clear answer.
"Enzo is a Chelsea player," Alonso said. "We are happy with him and he's getting ready for Monday."
The manager added that Fernandez has settled back into the group smoothly since rejoining training following the World Cup.
"I see him with a really good attitude and that's what we want," Alonso said, noting that the midfielder has "integrated really well" and is "training really well."
Fernandez joined Chelsea from Benfica for a then-British record £107m in January 2023 and has since become one of the club's most important midfielders, but his situation has remained a persistent subplot throughout the summer amid City's interest.
With the deadline for bids having passed unmet, Chelsea appear content to keep hold of him for the season ahead, regardless of any late approach from the Etihad Stadium.