Thomson, is highly-rated, and he currently manages Kelty Hearts.
Raith Rovers have also been strongly linked with a move for him to be their next manager.
He is a former Rangers, Middlesbrough and Hibernian midfielder.
There has been strong interest in the job at Pools with the club working their way through applications.
Pools chairman Raj Singh was asked about the manager search on Thursday.
He told the Mail: "It is all about opinion and all about debates, and the hard bit is for me. We will talk about it among ourselves and interview as many people as we can so it is a good process, then make a decision.
"A lot of people have applied for the job, as expected. We are just working through the applications.
"It is just a case of seeing the interested parties that have applied and going from there.
"Whichever manger we go for, we are not going to satisfy everybody.”