The legendary Hoops hitman believes that unearthing a ball-playing sweeper is a priority whether Dutch defensive ace Virgil van Dijk is prised away to the Premiership or not.
McGarvey also believes that Nigerian stopper Efe Ambrose is also not equipped to cut the Champions League mustard and has advised Lenny to think about relocating him next season.
McGarvey, who played 245 times for Celtic between 1980 and 1985 and scored 113 goals, said: "I believe Neil should make finding a commanding sweeper his priority.
"Celtic have proven very adept at unearthing talented players who are capable of making the step up to the Champions League and I am sure Neil will have a list of players he will be giving the once-over.
"But for me we are still short of a really commanding ball-playing centre-back and I say that whether Virgil van Dijk stays or goes."
When it comes to a summer departure for Dutch defensive master Van Dijk, McGarvey reckons he will be the stopper at the top of every English Premier League wish list this summer.
The former Celtic strike ace, who won two League Championships, two Scottish Cups and a League Cup with the Hoops, said: "Virgil van Dijk has been a fantastic signing for Celtic and if he does not make the World Cup with Holland it will be a travesty.
"But his quality and consistency both domestically and in the Champions League will have brought him to the attention of every boss in the English top flight.
"I would go so far as to say that, defensively speaking, Van Dijk will be the name at the top of their wanted lists. The good news for Celtic is that Virgil still has another two years on his current contract and quite frankly the club could ask what they want for him.
"But there is more at stake here in that Celtic have a lot of empty seats these days and the one thing they can't do is let another big player leave after letting Gary Hooper and Victor Wanyama go last year."
McGarvey is also adamant that Efe Ambrose is not good enough to fill one of the Celtic central defensive berths at Champions League level.
He said: "Unfortunately with Ambrose every time he makes a mistake in the Champions League it costs us a goal. The prime example of that was in the last 16 game with Juventus at Parkhead.
"So whether Van Dijk goes or stays we must get another top quality centre-back in.
"I like Ambrose and I think he has the athleticism to play sitting midfielder in front of the defence but Celtic just can't afford his errors at the very top level."