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Last week, the Reds rejected a £90m bid from the Spanish giants for the 25-year-old Brazil attacking midfielder, who then submitted a transfer request.
Coutinho has missed the opening two games of Liverpool's season with a back injury, but the club has repeatedly stressed he is not for sale.
Despite that, Barca have previously said they are "close" to signing him.
On Thursday, responding to Barcelona general manager Pep Segura's claim that a deal was close, Liverpool boss Jurgen Klopp said: "I don't know why other people are saying what they are saying.
"I don't even know them - especially this guy. I've never even met him."
The La Liga side have moved for Coutinho after selling Brazil team-mate Neymar to Paris St-Germain for a world record transfer fee of £200m.
Coutinho signed a new five-year deal at Anfield in January, which did not include a release clause.
He is also set to miss Saturday's home Premier League match against Crystal Palace (15:00 BST kick-off).
Liverpool's instant dismissal of Barcelona's third offer is further hard evidence of the determination within the club that they will not be forced into selling their prize asset under any circumstances.
Fenway Sports Group, and manager Klopp, remain unmoved by Barcelona's increased financial inducements - as well as a transfer request from a player who has clearly had his head turned.
Liverpool regard this latest bid, understood to be about £114m, as irrelevant because their stance, as it has been from day one, is that Coutinho will not be sold.
But questions remain. Will Barcelona take the hint and walk away? Will Coutinho, sidelined by a back injury, accept his dream move will not come to fruition and eventually return to the fold? Will his unhappiness increase at the prospect of a switch to the Nou Camp slipping away?
For all the noises coming out of Barcelona that a move is "close", it remains as far away as the day they made their first approach. Liverpool's mood has not altered.

It happened at 09.30 BST on Saturday at the junction of Cheapside and Bridlesmith Gate, blocking both roads.
Police cordoned off the scene but said clearing it was complicated due to overhead power lines. There are no reports of injuries.
Services were suspended between Nottingham Station and Royal Centre until shortly before 13:00 with continued disruption to the timetable.
A nearby branch of Barclays bank was evacuated as a precaution.

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James Ridley, riding Lookslikerainted, appeared to mistakenly think he had already crossed the finish line, allowing two horses to pass.
The Hunters' Chase at Newbury was eventually won by Triangular, closely followed by Ballytober.
Lookslikerainted, a 33-1 outsider trained by Martin Wilesmith, finished in third.
At the resulting inquiry, Ridley said the half-furlong pole caused the problem. Stewards ruled he was guilty of failing to ride out on a horse that would have finished first.
"Obviously I'm a little upset but compared to what happened in Westminster the other day it is absolutely nothing," Wilesmith said, after the attack in central London on Wednesday in which four people were killed and 50 people injured by Khalid Masood, who also died.
"I'm thrilled with the horse and just looking forward to when we can run him again now. We'll just look forwards. James has apologised."
Liverpool have rejected a third bid from Barcelona for Philippe Coutinho - believed to be in the region of £114m.
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A tram and a lorry have collided in Nottingham city centre.
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An amateur jockey who slowed down and lost his lead in the final stages of a race has been banned for 28 days.