The striker is a target for Arsenal ahead of the January market.
Asked if Rodriguez will stay, Le Tissier told the Daily Star: "I'd hope so.
"We aren't looking in too bad a shape this season - and Jay's still got to come back.
"If the seasons don't go well for the lads that have left, he could look at that and think sometimes the grass is not greener on other side and we can keep hold of him here.
"The club is in sound financial state right now.
"They did good business over summer and don't need to sell."
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