Wilshere - who spent last season on loan at Bournemouth - played the full 90 minutes in a 0-0 draw at West Ham, having been named in the Gunners' starting XI for a league game for the first time in 577 days.
The England midfielder is one of three high-profile Arsenal players with a contract that expires at the end of the season, along with Alexis Sanchez and Mesut Ozil.
But Wilshere, who has been clear about his desire to extend his career-long stay at Arsenal, does not have any renewal talks planned with manager Arsene Wenger.
"No, there's no update on the contract - we're in the same position as we were two weeks ago. There’s not really a date in the diary," Wilshere said.
"I've only read what he's [Wenger] said in the media. I've just played my first game in the Premier League, I'm concentrating on staying fit and staying in this team.
"That will look after itself. When it's the right time to talk about it, I'm sure the boss will call me and we'll have a chat.
"There's another game on Saturday, we'll see what the boss does, and at the moment that’s all I'm focused on. This time of the year is probably the most important time of the season."
Wenger singled Wilshere out for praise after a bright performance at London Stadium, but the 25-year-old felt he could have scored a decisive goal for his side, who sit seventh in the Premier League.
"I should have hit the target, there's no denying that and on another day I probably would have if it was on my left," Wilshere told Arsenal Player. "But it happened really quickly and it fell to my right and I swung at it and unfortunately didn't catch it right.
"But I felt good out there, I have been waiting for that chance for a while. I have played a few games in the Europa League and the EFL Cup and I've been desperate to play. I was happy to get the start and I thought I did alright.
"The Premier League is a bit different, a bit quicker than the Europa League or EFL Cup so it took some getting used to but I felt good, I felt free, I felt my touch was good and I linked up with the players well but there's obviously more to come."