Southampton were considered relegation candidates last summer when Adam Lallana, Luke Shaw, Calum Chambers, Dejan Lovren, Ricky Lambert and manager Mauricio Pochettino left St Mary's Stadium.
Koeman had a threadbare squad when he replaced Pochettino, but the Saints boss has bought wisely and his team surpassed last year's points tally with three matches to go.
Southampton now have 60 points to their name and could finish as high as fifth if results go their way on the final weekend of the season.
Regardless of how they perform against Manchester City on Sunday, Saints will finish with their highest points total since the 1984-85 season, when McMenemy led the team to fifth.
"Yes, he should win (manager of the year)
He's got my vote," said McMenemy, the club's most successful manager of all time.
"There are a lot of others being mentioned like Jose Mourinho, Sean Dyche and Eddie Howe, but Ronald has done a terrific job.
"Half the team walked out the door last year and something had to be done quickly
The best appointment they made was Ronald Koeman.
"He used all his connections and experience to get the right people in
He is a top man, the manager."
Although he has signed some stars from abroad, Koeman has also been keen to maintain Southampton's tradition of blooding youngsters in the first-team.
Academy products James Ward-Prowse, Matt Targett and Harrison Reed - among others - have featured for Saints this season.
McMenemy is happy to see Koeman carrying on with the policy he helped establish by scouting youngsters from Newcastle, Bath and London during his 12-year spell as Saints boss.
He believes the young players in Koeman's squad will get a chance to shine in next season's Europa League, provided they qualify.
"In the Europa League you need more players so the youth policy will carry on," said McMenemy, speaking on behalf of the The Football Foundation, which is celebrating 15 years of improving the country's grassroots football facilities.
"That is when you find out how strong they are, but the signs are good."
:: Lawrie McMenemy was unveiled as a Football Foundation Ambassador and was speaking at a visit to one of nearly 500 3G pitches the Foundation has delivered
Many of these pitches are used by professional clubs' community trusts' outreach work
Since its launch in 2000 the Foundation has supported 13,000 grassroots sport projects with grants worth £520m and leveraged £736m in additional partnership funding, thereby delivering schemes with a total project cost of £1.24bn
Source : PA
Source: PA