Chelsea had set a 5pm deadline for City to submit an offer meeting their roughly £120m valuation of the midfielder, warning that Fernandez would not be sold this window if it passed without an acceptable bid.
Maresca, who worked closely with Fernandez during his time at Stamford Bridge, confirmed City would not be doing business on the day itself.
"Not today, to be honest, I don't think we're going to do something today," he said.
The interest in Fernandez is tied to the uncertain future of Rodri, who returned to training for pre-season testing on Friday after back surgery, having missed the early part of the summer. Barcelona are trying to negotiate a transfer worth more than £60m for the World Cup-winning captain, who held talks with his own management on Friday over the direction of his career. Maresca declined to discuss the situation directly.
"I don't think it's good when people from other clubs speak about our players," he said, when asked about the speculation surrounding his captain.
Maresca also indicated more departures could follow. Tijjani Reijnders is closing in on a £52m move to Saudi Arabian club Al Qadsiah, while Savinho has made clear he wants to join Tottenham.
"We'll see what happens with some more, there is a change in this moment," Maresca said. "We are in a moment where players that were here many years have already left or others who probably can leave."
He added that some squad members were struggling to accept reduced playing time: "When they don't play, they struggle to understand or they struggle to see the reason why and I can understand that... Tijjani's situation is like James Trafford's situation and some more players."
Manchester City's Community Shield meeting with Arsenal on Sunday will be Maresca's first competitive match in charge.
Elsewhere, City's academy business continued at a lower level. Luton Town have re-signed winger Emilio Lawrence on a season-long loan, having already had the 20-year-old on loan at Kenilworth Road for the closing months of last season, when he made 21 appearances and scored twice, including in the Hatters' EFL Trophy final win at Wembley.
Luton manager Jack Wilshere said he had made his intentions clear to the player as soon as the previous loan ended: "From the last day of the season, I was clear with Emilio that my intention was to bring him back.
"He did well with us, so of course he then has more interest in him than he would have had last January.
"But I'm so happy that he sees us as a club where he needs to be to continue his development."
Lawrence, who is yet to make a first-team appearance for City, began his career at Everton before joining City in 2022 and has represented Scotland up to Under-21 level.