The Anfield ranks are already well stocked with creative attacking talent, but it has been suggested Jurgen Klopp would be open to bringing in another option.
Admiring glances are said to have been cast in the direction of Parkhead and a player currently working under former Reds boss Brendan Rodgers.
Forrest, who is a product of Celtic’s academy system and a Scotland international, is the man reported to have caught Liverpool’s eye, but Premier League suitors have been told the 27-year-old winger will be going nowhere for the figures being mooted.
Ex-Hoops striker Hartson told the Evening Times: “I have to say that I laughed when I saw the figures quoted for James Forrest this weekend.
“£8m? That might get you his big toe.
“Aside from the fact that the lad himself has signed a long-term deal with Celtic, the club he has been with since primary school, the money quoted for him is laughable.
“We are not talking about a pup at 16 or 17. We are talking about a boy who has scored goals at international and Champions League level and who has blossomed into a winger who guarantees double-figure goals.
“So spare me the £8m chat. If – and it is a big if – there was anyone looking at Forrest then they would need to triple that number just to get Celtic interested.
“The days of English clubs coming in and getting players for pennies are long gone. Peter Lawwell isn’t the type to let players slip out of the club without getting their market value and in Brendan Rodgers you have a guy who knows exactly what a player is worth.
“So you can forget anyone coming in for Forrest or any other player and taking them away for a song.”
Forrest has made more than 300 appearances for Celtic and remains on course to top the personal-best goal return of 17 he managed last season.
Hartson added: “There is a suggestion that Forrest will go on to become the most decorated Celtic player of the modern era and that will mean a lot to him too.
“But right now it is little more than chat.
“If Liverpool or anyone else want him then they will have to have very deep pockets.”
Forrest committed to a new four-year contract with Celtic in September 2018, with that deal intended to keep him in Glasgow for the foreseeable future.