Both Arsenal and Tottenham are keen on Parker's services, with West Ham ready to do business for around £10million for the Football Writers' Player of the Year.
But it is Wenger who is being urged to snap up the schemer by Dixon.
"He goes about his business in a workman-like way and that is not to say he hasn't got other aspects to his game. I think if you had taken his performances in a West Ham shirt last season, put them in an Arsenal shirt and replicated those displays, my old team would have got another ten points or so.
"I think the way he plays the game would suit Arsenal's style, to allow the more attacking players to flourish ahead of him."