Various landing spots are being mooted for a man seeing his future in the Spanish capital called into question.
Merseyside is not among those to have figured prominently in the speculation, with Manchester United and former club Tottenham considered to be more likely destinations.
It could, however, be that a Premier League scramble is sparked for a man who has previously illuminated the English top-flight.
If that is the case, then Jurgen Klopp has been urged to position himself at the front of the queue.
Quizzed on whether Liverpool should be interested in the 29-year-old forward, former Reds defender Matteo told Stadium Astro: “We certainly wouldn’t say no!
“Possibly. It’s a case of whether the financials could be done.
"It would be a big signing.
“If he was coming back to England, I’m sure that everyone would take him.”
Liverpool have first-hand experience of how productive Bale can be.
They faced him on a regular basis during his time at Tottenham and have also crossed his path since seeing the Welshman head for Madrid.
He started a meeting between the Blancos and Liverpool in the 2018 Champions League final on the bench, but entered the fray to score a stunning overhead kick.
It is that ability to produce moments of match-altering brilliance that Matteo believes should have Klopp among those pursuing a prized signature.
He added: “With Bale, when Madrid beat Liverpool in the final, he had that bit of X factor.
“Liverpool could maybe do with one more X factor player to score in the finals.
“That’s what we’ve lacked that bit of X factor to get us over the line.”
Klopp has suggested that there will be no more elaborate spending from Liverpool over the summer, following a sizeable outlay in 2018, but the right additions could tempt him back into the market.
Bale would tick plenty of boxes, but the Reds already boast the likes of Roberto Firmino, Mohamed Salah and Sadio Mane on their books – although the latter is being linked with a move to Madrid.