Despite being linked with a number of top European clubs, including Real Madrid and Inter Milan, Auguste expects the 29-year-old to stay put.
The Frenchman signed a contract in February worth an estimated £125,000 a week which is due to run out in 2021.
Payet moved to West Ham last summer in a £10.7m transfer deal but in light of his fantastic form throughout the past year and at Euro 2016, his valuation is expected to have risen towards the £60m mark.
Speaking to the Guardian, Auguste said: “He has a great contract with West Ham so I cannot see him leaving. Dimitri is happy in London.”
“You never know in football but only West Ham know what price they want if they decide to sell him.”
On the back of an outstanding season at West Ham, in which he scored 12 goals in all competitions, Payet was named in the PFA Team of the Year and has emerged as one of Europe’s most highly-coveted players.
Real Madrid manager recently Zinedine Zidane praised the player as “one of the most important players in Europe” who could “improve any side”.
The Spanish side have a history of talking up their transfer targets before moving to sign them as they did with Luka Modric and Gareth Bale.
But Madrid are not alone in their interest after Inter Milan openly expressed their desire to bring the Frenchman to the San Siro.
“As a fan, I would love to see Payet in an Inter shirt,” said the honorary president Massimo Moratti.
“We are missing two to three players to be competitive. The important thing is to have solid players that ensure continuity.”
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