A deal for Alexandre Lacazette to join Arsenal may persuade Alexis Sanchez to stay at the club, according to Nigel Winterburn.
Lacazette completed a medical ahead of a £52m switch from Lyon on Tuesday, according to Sky sources.
Sanchez has yet to reveal whether he will extend his Arsenal contract which expires next summer, and Winterburn believes it is crucial that Arsene Wenger retains his attacking players.
"I think it was obvious to Arsenal fans and to Arsene Wenger that one of those areas to strengthen is the centre forward position", Winterburn told Sky Sports News HQ.
"I am hoping Giroud will stay, I still feel he is valuable to the team as well. Arsenal know they need quality to help them challenge for the title."
Winterburn added: "I hope the Lacazette deal leaves [Sanchez] at the club. He can play on the left, up front or in the hole.
"Arsenal cannot afford to bring in Lacazette then two weeks later Sanchez leaves.
"I am hoping Wenger can persuade him to stay for another season, see what happens with the team then sign a new contract."
Giroud played down talk of a summer transfer away from Arsenal by insisting he wants to "carry on his good journey" at the club.
Arsenal won the FA Cup last year but finished in fifth place in the Premier League, the first time they have failed to qualify for the Champions League since 1997.
And Winterburn, who played for the club from 1987 to 2000, believes they need at least two more signings to challenge for the title.
"I am hoping they will back that up with a couple more major signings," he said. "If you look at the end of last season Wenger said he thought the team was strong enough to challenge for the title.
"Over the last two seasons that hasn't proven to be the case.
"There becomes a point when you have to start mixing it up, maybe one or two players will move on and you bring in fresh faces and set new challenges."
Arsenal begin their Premier League campaign against Leicester City.