It was reported that convicted rapist Ched Evans was to train with them with a view to playing. But the League One club said: "Oldham Athletic are aware of newspaper reports linking the club to Ched Evans."
They added the club "will not be extending an invitation for Ched Evans to train with Oldham Athletic nor will we be offering him a contract".
Sheffield United had agreed to allow Evans use their training facilities after his release from prison in October.
But the Bramall Lane club were heavily criticised for the move and retracted their offer in November.
TV presenter Charlie Webster, sixties pop star Dave Berry and Sheffield businesswoman Lindsay Graham all resigned as patrons of the club after Evans was invited to return to training with the Blades.
Musician Paul Heaton also stood down as a patron of the club's community foundation, while Olympic champion Jessica Ennis-Hill stated that she would want her name removed from one of the Bramall Lane stands should Evans play for the club again.
Shirt sponsor DBL Logistics also threatened to end its backing of Sheffield United should Evans sign a contract to play.
Oldham courted controversy back in 2007 when they offered convicted killer, Lee Hughes a contract, after he was released from jail after causing death by dangerous driving. Hughes went onto play for Notts County, Port Vale and Forest Green Rovers after becoming a crowd pleaser at Boundary Park.
When Oldham signed him the club asked supporters "not to pass moral judgement". His reported salary of £1,800-a-week at Boundary Park was less than a 10th of what he earned at the peak of his career with West Bromwich Albion.