The 25-year-old, who has endured several injury-plagued years, is out of contract at the end of the season.
Arsene Wenger has previously stated that Wilshere must prove his fitness in order to be offered a new contract, and the midfielder has started the club's last four Premier League fixtures.
In Thursday's 3-2 win over Crystal Palace, the England man played a major part in Arsenal's third goal with an excellent pass for Alexis Sanchez to control and finish.
When asked about his contract situation, Wilshere told reporters: "We'll see when [Wenger] speaks to me but I'm sure it will get done, yes."
The former Bournemouth loanee also spoke of his fitness and love of the game, adding: "I was happy with my form last year. I'm probably playing better now. I feel fitter and I am enjoying my football."
Wilshere has been with Arsenal since the age of nine and has made a total of 177 senior appearances for the Gunners.