Andy Carroll is on the brink of joining West Ham permanently after passing a medical with the Premier League club.
Brighton have threatened to take action against the LMA as the dispute with Gus Poyet rumbles on.
Kiernan had a temporary spell at Griffin Park in November, making seven appearances for Uwe Rosler's side before returning to the Latics.
The Republic of Ireland Under-21 international featured in both central defence and midfield and played a key role in Brentford's win over Sheffield United in late November, helping to set up the first goal.
He is available for selection for the Bees' League One game at Oldham on Saturday.