Matthews has been linked with a potential move to EFL Championship outfit Portsmouth, with Talay confirming the young defender will not be available for the Friday night match against Melbourne Victory.
The 20-year-old's looming move comes after a breakout 2023-24 season, which earned him his first Socceroos call-up under coach Tony Popovic.
Hayden Matthews in action for Sydney FC. (Dean Lewins/AAP PHOTOS)
"Hayden is currently overseas," Talay said on Thursday.
"Pending certain things get ticked, the club's come to an agreement with another club."
Should Matthews make the move to Portsmouth, he will join forces with former A-League players Thomas Waddingham (Brisbane Roar), Kusini Yengi (Western Sydney) and Jacob Farrell (Central Coast).
A Sydney FC academy product, Matthews has featured in 29 league matches for the club across two seasons.
The young gun made his international debut against Bahrain in November.
Hayden Matthews has shown his ability with Sydney FC in the A-League Men. (Masanori Udagawa/AAP PHOTOS)
His departure leaves Sydney needing to replenish their defensive stocks, with loan player Alex Popovic's future at the club up in the air.
Popovic is due to return to parent club Gwanju in the K-League, but the Sky Blues are determined to lengthen his stay.
Teenage talent Nathan Amanatidis has already departed for Brisbane Roar, while out-of-favour midfielder Max Burgess is likely to leave at the end of his contract in June after attracting interest.
"We're very close," said Talay on contract talks with Popovic.
"There's discussions happening with 'Popa', so we're very close with that.
"At the same time, we're still looking to bring in another central defender as well."
Fellow youngster Ariath Piol has left Macarthur FC to pursue his own overseas opportunity.
The 20-year-old forward has been heavily linked with MLS outfit Real Salt Lake in the United States.
Piol also debuted in the 2023/24 season and has scored four goals - including one with a spectacular bicycle kick - across 11 matches for the Bulls.