Tarkowski has impressed this season, helping Burnley finish seventh and earning a standby spot with England for the World Cup.
One interesting wrinkle to the Tarkowski to Liverpool transfer speculation is the fact he is a Manchester United supporter, and has not been shy about it.
Tarkowski though has previously admitted this would not prevent him signing for Liverpool, when he was asked about it four years ago.
The centre-back was playing for Oldham Athletic at the time.
He told The Mirror: "I am a United fan, The Class of ’92 were my heroes.
“I was born in ’92 and grew up watching them. But, if there was a chance to go to Liverpool, I’d definitely look at it!"
Tarkowski added: "I believe in my ability and, hopefully, my time will come at some point."
Four years on he is achieving his ambitions, starring in the top flight and on the fringes of the international set up.
A move to Liverpool would take him to the top level and allow him to star in the Champions League.
It certainly seems he would set aside his United fandom to pursue this.