Hennessey has a year left on his Crystal Palace contract, while the Toffees are down to just one senior 'keeper.
Southall in action for Everton
Howard is returning to his native United States after a decade at Goodison Park, leaving Joel Robles as the club's only senior shot-stopper.
Howard's departure has left Joel as Everton's only senior 'keeper
And Southall, who played 750 times in 17 seasons at Everton, claims to have urged his old side to buy his fellow Welshman, the Crystal Palace number 1.
"I like Wayne," the 57-year-old told Tuesday's Colin Murray show (c. 12:37). "I told Everton to buy him but obviously, like Everton, they don’t listen to anything I say.
"I think he’s got everything he needs to be a top-class goalie and I’d be quite happy to see him sign for Everton.
Hennessey following Palace's FA Cup final defeat
"He’s had an up-and-down season but it’s his first major one in the Premier League so it was never going to go fantastically all the time. Moving to Palace he’s going to be busy but I think it’s a good stepping stone for him."
56-cap Hennessey, who is Wales first choice ahead of Euro 2016, arrived at Selhurst Park from Wolverhampton Wanderers two and a half years ago.
However, the 29-year-old found first team opportunities few and far between before the 2015-16 campaign, in which he appeared 38 times in all competitions.
The Palace shot-stopper is off to France with his country
Hennessey is under contract in south London for another 13 months, and Palace could opt to cash in this summer rather than lose him on a free transfer.