Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
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.