Bolt has long expressed his desire to play professional football and hopes to secure a contract with the Australia A-League team following the trial period. "We regularly receive similar approaches".
But Bolt's agent has confirmed he opted against taking up their offer.
The former sprinter, who holds the world record in the 100 metres, 200 metres and 4×100 metres relay, has been training with Australian club Central Coast Mariners as he bids to start his football career.
Bolt is ineligible for that fixture, and likely all the Mariners' matches until January 3, 2019, when the league's next registration period opens.
Just seven weeks into trialling with the Mariners, based north of Sydney, Bolt has yet to sign with the club but grabbed global headlines on the weekend after scoring two goals in a trial match. It is believed that the Football Federation of Australia would need to contribute to any contract offer from the club to make it economically feasible.
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Everyone stayed at his own house and I think the players, when they woke up in the morning from that they read (reports) on social media.
"I saw him play".
"I'm really not interested in it (contract speculation) to tell you the truth", he told reporters.
He scored two goals in a pre-season fixture last week and rejected a two-year deal from an ambitious Maltese side bankrolled by Saudi billionaires.
Postecoglou, who won back-to-back A-League titles as coach of Brisbane Roar, said "good on" Bolt for trying but the 53-year-old was quick to underline the scale of his task.
Mariners coach Mike Mulvey was reluctant to talk about Bolt on Thursday, adding he was not involved in negotiations.
Mariners captain Matt Simon dismissed suggestions the chronicles of Bolt were distracting the squad ahead of their A-League opener.