Southall, Everton's record appearance maker with more than 700 games, branded the offer 'stupid' and 'disrespectful' considering new United manager David Moyes managed the Toffees for more than 10 years.
"The joint bid stinks," said Southall as quoted in the Daily Express. "The way David Moyes has gone about it stinks. The entire world knows Marouane Fellaini and Leighton Baines are worth a lot more than the £28m offered and Moyes is disrespecting Everton.
"If you've got a good relationship with the club and you're supposedly best mates with the chairman - and Moyes was always saying how they were when he was at the club - would you go back to you mate's business and try to pinch them off know that the business is skint?
"It's really despicable behaviour towards Everton and disrespectful towards the fans.
"The stupid offer - and it is a stupid offer - isn't entirely down to him, but he shouldn't go in with an offer that seriously undervalues the players just to unsettle them.
"Doing it this way stinks. It wouldn't have happened under [Sir Alex] Ferguson.
"There's a real danger he will lose all his credibility with the Everton fans. He might think that in order for him to succeed he is entitled to go for players he knows and trusts but he can still operate ethically.
"The manner in which it's been done is rubbish.
"If Baines goes, our chairman will be lynched. It's the equivalent of telling the Everton fans 'stuff you, we're not interested in what you think, we want the money.'"
Reports claim United are prepared to go back in for the Everton duo with a £35m bid. Moyes has come under pressure for a lack of transfer activity at Old Trafford - Cesc Fabregas and Thiago Alcantara have both been linked but neither joined.
But they got their Premier League campaign underway with a promising 4-1 win over Swansea at the Liberty Stadium.
Robin Van Persie and Danny Welbeck scored the goals, but United are still thought to be keen to strengthen their central midfield.
Options currently available to Moyes include Michael Carrick, Anderson and Tom Cleverley but the Old Trafford manager is believed to be on the look-out for another box-to-box midfielder.
Do YOU want to write for GiveMeSport? Get started today by signing-up and submitting an article HERE: https://www.givemesport.com/writeforgms