The 36-year-old former Manchester United and Roma defender has been without a club since his contract at Al-Fayha in Saudi Arabia expired on 30 June, and Valencia's technical staff at their Paterna training ground have identified him as one of the strongest free-agent options available, according to Marca.
Sporting director Braulio Vázquez inherited a squad short of defensive solidity from predecessor Ron Gourlay's summer planning, and Valencia's finances leave little room to manoeuvre before the transfer window reopens in January.
That makes a free-agent addition like Smalling especially attractive, since the club retains a spare squad registration that could be used without paying a transfer fee. Valencia's priority is understood to be a defender who can bring calm and composure to a side that has lacked a reliable presence at centre-back.
Smalling spent two seasons at Al-Fayha after five years in Serie A with Roma, making 64 league appearances in Saudi Arabia and avoiding any serious injuries during that time, a durability record that stands in his favour with Valencia's medical staff. He previously spent a decade at Manchester United after starting his career at Fulham.
Braulio is not treating the move as urgent, and will continue to explore other options before committing to any single name, with Valencia keen to find value in a market where they have almost no money to spend this winter.