The Liverpool Echo says Brentford manager Uwe Rosler is pursuing a permanent deal for Everton's England U-19 defender Bidwell - just weeks after he completed the signing of Toffees midfielder Adam Forshaw.
The pair have both spent time on loan at Griffin Park last season and played regularly under the tutelage of former Manchester City striker Rosler.
Rosler said: "It is no secret that we would like to get Jake back to Brentford - whether it would be on a season-long loan or permanently is out of our hands.
"David Moyes is now on holiday. They know we are very keen, but you can't push everything in the first three or four weeks - good things come to those who wait.
"But I have said all along that most of the time we bring players in on loan we want to sign permanently, as we have seen with Adam Forshaw and Harlee Dean, because we don't want to keep starting from scratch."