The man who guided Saints to their 1976 FA Cup win and a second placed top flight finish, believes there is a greater chance of loyalty from a British manager than a foreign import.
With Mauricio Pochettino quickly ditching Saints for Tottenham, and Koeman moving to Everton after just two seasons at St Mary’s, McMenemy says he would be happy with a manager like Eddie Howe, Steve Bruce, Mark Hughes or even Alan Pardew, who are more likely to plan for the long-term.
Writing in his exclusive column in today’s Daily Echo he said: “Hand on heart, certainly with the experience we have had with our last two managers and what is happening elsewhere, I would like to see a British manager.
“These days managers and players from other parts of the world are ready to move every two or three years, whether they are successful or not.
"In my day with messers Clough and Robson etc we just wanted another contract, and, though the money earned has changed, I think that is still the mentality of British managers generally.
"As was proven at all of our clubs in the past, we all had tough times such as relegations, not followed by the sack but support, which in the long term was repaid by cup wins and high positions in the league etc.
"I think British managers are aware putting in 100 per cent, and knowing the business as they do, that directors and supporters will be more supportive and prepared when they see the effort put in to stand by when the bad times are there, waiting for the good times.
"At present there are so few around but the names mentioned I wouldn’t knock back at all.
"Eddie Howe, obviously, but I am sure Bournemouth will hold on to him as tight as possible.
"Steve Bruce, four years at Hull with ups and downs and who has got them back in the Premier League, but it appears from a distance things may not be settled as after winning promotion he said he needs to look at his future.
"Mark Hughes at Stoke City. With due respect to them Southampton are a bigger club, but Stoke have an owner, Peter Coates, who will do everything to hang on.
"Even Alan Pardew, who wherever he has been has done a good job.
"I am sure the supporters I listened to would not mind a British manager coming in whether we stay in Europe or not."
- Read Lawrie's full column, including his thoughts on Ronald Koeman, in today's Daily Echo