Lacazette has been linked with a move away from North London after entering into the final year of his contract.
The 30-year-old joined Arsenal from Olympique Lyon in the summer of 2017 and scored 13 goals in 31 Premier League games last season.
It remains to be seen whether Lacazette will be offered a new contract by Arsenal but Winterburn would like the Frenchman to stay at the Emirates Stadium unless an upgrade is found.
"Arsenal shouldn’t sell Lacazette unless they’ve got an upgrade in place. I wouldn’t let him go until we have secured another striker. I’ve said that all along,” Winterburn told Goal.
"Lacazette is a different striker to anything Arsenal have at the club. When he’s in top form, he holds the ball up well, his link-up play is good.
"I suppose his strike rate is not the very, very best of what you want, but then we are not at the very, very top of the league either at the moment as well.
"So personally, at the moment, I don’t want to see him go, unless we’ve got someone coming in that’s going to excite me.
"I wouldn’t let him go and then we haven’t got anybody else to bring in. For me, that’s just way too risky."
