Harrison, who joined Leeds on a permanent deal from Manchester City last summer, grabbed ten goals and two assists in all-competitions last season, including his strike against Brentford on the final day of the season that secured survival for Jesse Marsch’s side.
Their transfer business in January favoured experience to help the team in their survival bid, one that proved dividends by the end of the campaign as Newcastle ended the season in 11th place - 14 points clear of danger.
Jose Enrique, who played over 100 games for the Magpies, believes that the job Eddie Howe has done at Newcastle should mean he is given the freedom to bring in the players, like Harrison, that would best fit his vision for the future.
He told Genting Casino: “If Eddie believes he’s the right player for Newcastle, I believe it.
“Klopp won the manager of the season but Eddie is right up there with him and if Harrison is a player that he wants, then they should sign him.”
He added: “It would be a massive mistake for them to go for Neymar or Pogba.
“I don’t think Eddie Howe will go for these kinds of players.
“Pogba doesn’t suit Newcastle and Eddie Howe will look for a more aggressive, high-intensity player.
“It will be similar to when Man City signed Robinho, it didn’t work out and I know the fans would love these players, but they’ll go for the money and not the project.”
Check out the latest Premier League transfer speculation below...
5. Toon lead Rabiot race
Newcastle United and Chelsea in pole position to sign Adrien Rabiot from Juventus this summer. The player could be sold for as little as £12.8m. (Corriere dello Sport) | Getty Images
6. Spurs join Mamardashvili race
Tottenham Hotspur have joined Manchester United in their pursuit of Valencia shot-stopper Giorgi Mamardashvili. (Marca) | Getty Images
7. Magpies plot big money Diaby swoop
Newcastle United would be willing to break their transfer record and pay over £50m for Bayer Leverkusen winger Moussa Diaby this summer. (90min) | Getty Images
8. Cucurella on City radar
Manchester City are looking at a potential summer swoop for Brighton defender Marc Cucurella. (Telegraph) | Getty Images