A two-year contract offer is on the table, but it remains unsigned.
Arsene Wenger has come under intense scrutiny in recent weeks following the capitulation against Liverpool and Bayern Munich.
Several top European managers have been touted to replace Wenger, including Juventus boss Max Allegri.
Although Hoddle senses Wenger’s time at the Emirates might be coming to an end, he thinks a stand named after him would be a befitting honour.
“I know Arsene very well, he’s a friend of mine, Hoddle told ITV’s Champions League highlights show.
“I have immense respect for him as a manager and a person.
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Arsene Wenger's future is up in the air
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Glenn Hoddle thinks Arsenal should name a stand after Arsene Wenger
He deserves a stand to be named after him. That’s how he should be going out
“He’s a fantastic guy. He needs to go out with the respect he’s earned over the years.
“For him, if he has got jobs to move onto, it might be time to go now and get the club united.
“He deserves a stand to be named after him.
“That’s how he should be going out if he goes at the end of the season.”
Arsenal face Lincoln next in the FA Cup quarter-finals on Saturday (5.30pm).