Wilder has led Sheffield United to third in the Championship this season, having won promotions from Leagues One and Two with the Blades and Northampton Town respectively during the two previous campaigns.
But despite five Premier League positions having opened up since August, Wilder is not thought to have been approached about any.
Three of those jobs have since gone instead to former Premier League managers - Roy Hodgson, Claude Puel and David Moyes - with West Brom and Everton yet to fill their vacant posts.
The Baggies have, however, been strongly tipped to appoint another in Alan Pardew, and Jenas - the former Aston Villa and England midfielder - told the BBC's Match of the Day on Saturday: "You know exactly what you’re going to get (with Pardew).
"It might be a good start, will that then fade out? I’d like to say somebody take a risk, I really would. You’ve got managers like Chris Wilder doing a fantastic job at Sheffield United.
"It really is (the fear of going down), and everyone’s playing the safe game."
Another ex-England midfielder, Ray Parlour, told Talksport last week that Wilder should ignore any interest that may arrive from West Brom.
"Why does he want that?" said Parlour. "What he’s achieved at Sheffield United is superb.
"Sheffield United is a big, big club - I think he’s got every chance of getting them up again. Three back-to-back promotions would be amazing as a manager."
This is only Wilder's second ever season above the fourth tier as a manager, having learned his trade at Alfreton, Halifax and Oxford United.