The La Liga giants have already seen two offers for the Brazilian knocked back, with £90m not enough to tempt those at Anfield into a sale.
Barca are refusing to throw in the towel, though, and could test Liverpool’s resolve with a third approach before the summer window closes - as they continue to seek a replacement for the departed Neymar.
Collymore believes Jurgen Klopp should be open to selling if Coutinho’s value continues to rise as a big-money deal would allow Liverpool to re-invest elsewhere in their squad.
The former Reds striker wrote in a column for the Mirror: “If Barcelona bid anywhere near £110 million or £120m for Philippe Coutinho and Liverpool don’t sell then, I’m sorry, but my old club are being barmy.
“And with a bit of clever thinking and some shrewd business then with that sort of dough there’s no reason why Jurgen Klopp and Co can’t build a side to rival any of those three.
“What will probably happen if Liverpool do relent and sell Coutinho to Barcelona is that they will sink £60m each into the signing of two players.”
Coutinho is yet to figure for Liverpool this season amid the ongoing transfer talk.
He has handed in a transfer request in an effort to force the issue, while a back problem kept him out of a Premier League season opener against Watford.
The 25-year-old has also been left out of Klopp’s squad for the first leg of a Champions League play-off tie against Hoffenheim on Tuesday.