The 26-year-old tried to orchestrate a move away from Merseyside during the summer window citing a desire to play in the Champions League, but an exit was blocked by the Reds.
Despite his desire to leave, Ayre has insisted that Suarez is an "important part" of the Premier League outfit's future, and had no doubts that the controversial Uruguayan would stay put.
"We genuinely always wanted Luis to be here this season," Ayre told Sky Sports News. "We wanted him to continue to be here, continue to contribute because he's such a brilliant player. We're not a selling club. We're here to win and move forward and we see Luis as an important part of that."
"At the appropriate time we will have [contract] talks with Luis and his advisers. I'm absolutely certain in the summer or approaching the next summer, we'll have a conversation with Luis."
Ayre also insisted that he has no ill feeling towards Arsenal following their summer bid of £40,000,001 for Suarez, who returned to action after a 10-match ban in last night's 1-0 defeat to Manchester United in the third round of the Capital One Cup.