The Reds were said to have made a surprise bid for the 23-year-old during Euro 2024 but withdrew when Newcastle requested Jarell Quansah as part of the deal.
Gordon caught the eye after an impressive season at St James' Park, during which he scored 11 goals and provided 10 assists in the Premier League.
His impressive performances for the Magpies earned him a spot in Gareth Southgate's Euros squad, though he only played five minutes as a late substitute in the goalless draw against Slovenia.
While Liverpool may still make a new approach for the attacker, Howe has once again made clear that the former Everton man is not for sale this season.
Howe confident over Gordon's future
Speaking to the media earlier this week, Howe said: "He's [Gordon] an integral part of what we're doing. We've had no conversations over the summer where it has been fractious or negative.
"He's always been the Anthony Gordon who has given absolutely everything to Newcastle and I want to make that clear to all our supporters.
"Anthony needs a bit of a break but by the time he comes back, he'll be ready to go. He's such an important player for us.
"We didn't want to lose anybody. Why would we want to lose our best players? We fought really hard to make the right decisions but in those last few weeks it was very, very difficult," the Newcastle boss added.
Gordon, who has two years remaining on his Newcastle contract, is currently on a summer break after his time with the England squad at Euro 2024.
TEAMtalk report that the Magpies are likely to try and tie the 23-year-old down to a lucrative new deal once he returns from his holiday.
Slot comments on Liverpool transfer activity
The summer transfer window has been very quiet for Liverpool, with the club yet to make a signing, while the likes of Joel Matip, Thiago Alcantara and Adrian have left Anfield this summer.
The Reds are currently on their pre-season tour in the US and it will be the first opportunity for Arne Slot to assess his current squad and identify areas that need strengthening.
Slot was questioned by journalists about the Reds' lack of transfer activity this summer ahead of their opening match against Real Betis in Pittsburgh.
He responded: "Like I said, we already have a very good team I'm already really happy with.
"But it would be a surprise for all of us I think if we don't bring any player in, so that will probably happen in the end. But for now, we are just waiting for the players to come back and waiting for the right ones to sign."
Liverpool have been linked with moves for Benfica starlet Joao Neves, Takefusa Kubo of Real Sociedad and Sporting Lisbon centre-half Goncalo Inacio this summer.