The winner of eight Olympic sprinting titles, who retired from athletics in 2017, is currently on trial at Australia's Central Coast Mariners.
Bolt, 32, scored two goals in a recent pre-season friendly but has not been offered a contract.
"Usain does not wish to pursue this Malta opportunity," said his agent.
"There is a lot of interest in Usain playing football," Ricky Simms also told ESPN. "We regularly receive similar approaches."
In response, Valletta chief executive Ghasston Slimen said: "We wish Usain Bolt all the best with his football career. The Valletta FC offer is always on the table."
Australia's Daily Telegraph reported that Bolt and Mariners chief executive Shaun Mielekamp spoke about the Jamaican's future at the A-League club, who begin their domestic campaign on Sunday.
The Mariners are said to be waiting for governing body Football Federation Australia to decide whether it will contribute to a potential $3m Aus (£1.63m) offer to the 100m and 200m world record holder.
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