The 21-year-old central defender joined the Bees on a permanent deal in January but was due to return to Boundary Park when the loan window reopened this weekend on a 28-day contract.
However, given Harlee Dean has been struggling with a groin problem recently and fellow central-defensive partner Tony Craig is soldiering on with a broken hand, Brentford boss Mark Warburton has vetoed Tarkowski's Latics return.
"Harlee and Tony have been our first-choice centre-halves, they've done outstandingly well over the last two seasons," Warburton told Bees Player.
"James would have played at Oldham and maintained his fitness and we would have had a call (to make) after 28 days.
"Right now Tony - with his hand - has done great but we have to be aware of the situation and Harlee has been back from injury and we have to be aware of that.
"From our point of view we have to make sure all bases are covered here and give ourselves the best chance every fixture. James is joining us, he'll train this morning (Saturday), he's one of us now."
Latics boss Lee Johnson had been hoping to include Tarkowski in his ranks for the visit of Bristol City on Saturday.
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- Harlee Dean
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