Sources say Daniel Levy, chief executive of English National Investment Company (Enic), through which Mr Lewis holds his stake in Rangers, has been knocking on doors in the City and elsewhere to sound out bankers about potential investments in European football clubs.
His timing is ripe, as outside investors queue to buy stakes in top-flight European clubs, many of which are preparing to float, some of them in London.
Italian clubs preparing a London offering include AC Milan, and Juventus - currently top of Serie A, Italy's equivalent of the Premier League.
AC Milan has appointed ABN Amro Hoare Govett as the stockbroker to the deal, and Lehman Brothers as its financial adviser. The club, currently off the pace in the Italian league, has been tagged at pounds 500m, making it worth substantially more than Manchester United, with a stock market value of pounds 416m.
Two other Italian clubs, Lazio and Fiorentina, have also expressed a desire to list in London, while PSV Eindhoven, and Paris St Germain are among other members of the European elite that may float.
Mr Lewis has substantial funds available to broaden his exposure to football. After selling the family catering concern, he has added to his wealth by astute dealing in the foreign exchange market, where he is one of the biggest private players, and is rumoured to have made more out of Black Wednesday than the pounds 1bn that George Soros, the international speculator, is thought to have earned.
Enic, a quoted investment trust, saw a steep rise in its shares after Mr Lewis purchased his stake in Glasgow Rangers. From 100p, the shares climbed to a peak of 257p, and are now 223p. The deal valued Rangers at pounds 160m.
Mr Levy said that he could not comment on any deals Enic was currently discussing. But he said that the investment in Rangers was taken for purely business reasons, and its chief attraction was that, next to Manchester United, the club has the second strongest brand in British football, with a huge overseas following.
While the club is well known to football fans on the continent, and has a strong network of overseas supporters clubs, European honours are meagre. Despite its ambitions and status, the only European silverware to its name was a solitary European Cup Winners Cup from the 1971-72 season. This year, it has been knocked out of the European Cup after some less than compelling performances.
Although Rangers' income from Sky was only pounds 1m last season, Mr Levy said he expects this to rise as pay-per-view TV becomes a reality, and a European Super League comes closer.