The Hammers captain believes the French star will stay because he loves the club.
Payet is a player in high demand after a superb debut season in England at Upton Park which saw him rack up 12 goals and 12 assists and establish himself as a leading star for the French national side.
His stock has only risen with his performances so far at Euro 2016 in his home country, with the 29-year-old setting up Olivier Giroud for the first goal of the tournament and striking a stunning last-minute winner against Romania in the opening group match.
That form has led to increasing speculation that a single season is all that West Ham fans will get of their new hero, with numerous top clubs from around Europe said to be interested in the star's signature.
However, Noble is confident that Payet will turn down any interest to give the Irons another year because of his "love" for the club and his teammates.
When asked by Sky Sports whether he was expecting Payet to be at the club next season, Noble replied: "I think he will be. I've been in a lot of contact with him over the summer and he loves the football club.
"But football is football, so you never know, but obviously we'd all like to see him back here in the summer."
Keeping hold of Payet would be a huge boost for West Ham as they look to build upon last season's seventh-place finish and become true European competitors.
They have already strengthened their midfield hugely with the additions of Havard Nordtveit and Sofiane Feghouli, but they are likely to want to build their side around Payet's ability once again as they aspire to launch an all-out assault on the Premier League's top four.