The Danish forward and the Italian defender did battle in Italy, although neither seems to remember it. But one or the other should enjoy an unforgettable evening at Parkhead tonight when Celtic and Rangers meet in a live televised Tennents Scottish Cup quarter-final.
Annoni, Celtic's cut-price buy from Roma last month, is poised for an Old Firm baptism against Laudrup, either at right-back or in a back three. "I can't really remember him, although I played against Roma a few times for Fiorentina," recalled Laudrup, although Annoni said the contest came when he was at Torino.
"Italian defenders are always tough. They play to the limit and sometimes even beyond it, but I'm sure it won't be any different for me from facing a Scottish defender," Laudrup added.
Annoni, known as "Tarzan" in Rome and the scariest-looking defender to arrive in Scotland since Hearts signed another Italian, Pasqaule Bruno, was non-committal on the prospect of trying to tame Laudrup who, along with Celtic's 28-goal Jorge Cadete, is a leading candidate for the Player of the Year award in Scotland.
"When I joined Rangers in 1994 people told me about the Old Firm game," Laudrup said. "I went into it understanding what a local derby can mean in a big city and you only have to experience it once to understand what it means to people here.
"I've played in a number of them now and they are still unique occasions. But they are the games I want to play in as a player because there will be 50,000 there and millions watching on television. You enjoy them if you win them, of course. There is a lot of pressure on the players and manager but I still look forward to them."
Rangers fans will be looking to Laudrup for inspiration again, with Paul Gascoigne still unfit because of the ankle injury he sustained in the Amsterdam six-a-side tournament which kept him out of England's defeat by Italy on 12 February. Gascoigne is expected to have the plaster removed at last today.
"If he gets the go-ahead from the specialist there is a possibility he could still be fit for the Premier Division match against Celtic on March 16," Walter Smith, Rangers manager, said.
Smith has still heard nothing official from Sweden's captain, Jonas Thern, who has been quoted as saying he will accept a two-year contract to join Rangers in the summer. "If that's his decision I will be delighted, but as yet we haven't heard from him officially," Smith added.
Meanwhile, Dundee United's manager, Tommy McLean, paid tribute to his team after a hat-trick of Bell's Manager of the Month awards. McLean has won the accolade for the third month in a row after a superb run of form by United.
"I am delighted with this award and it is fine recognition for the efforts of the players at Dundee United in recent weeks," McLean said. "To win three in a row shows that we have achieved a degree of consistency which is what everyone strives for in football."
It is the first time such a feat has been achieved since the inception of the awards by the Scottish League's sponsors.Reuse content