Ex-Chelsea captain Hazard is being linked with a return to London this summer after three injury-plagued seasons in Spain.
For Winterburn, while not doubting the Belgian's talent, the midfielder's injury record is just too big a gamble for the Gunners.
"But the one that's gone to Real Madrid and hardly played because of these injuries, then no it wouldn't be a good signing.
"I haven't seen him around that much and I don't know if that's a serious transfer that could happen.
"Arsenal do need to improve their squad numbers, but with Hazard would he be expected to play all the time and who's position does he take."
Indeed, Winterburn believes Gunners football chief Edu should prioritising other areas of the pitch this summer.
He continued: "You do want that competition for places so it is interesting to see if it would happen, but I'm more interested in what Arsenal are doing in other positions, then worrying about Hazard coming or out.
"It's very much a wait and see with Arsenal, we seemed to be linked with everybody who could become available."
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