Sven-Goran Eriksson has never said he would make an offer for the England international, but he did say "I'm sure every Premiership manager would be interested if a player like Michael became available".
However, he is to step up his search for a striker with Peter Crouch, Nicolas Anelka and Jefferson Farfan linked.
The former England coach has been on a trip to Asia over the international break, but it is claimed he will return this week and immediately start his scouting mission to bolster City's forward line during the January transfer window which opens in six weeks' time.
Eriksson will attend the England versus Croatia Euro 2008 qualifier at Wembley on Wednesday, where Liverpool's £8million-rated Crouch will be under the spotlight.
It is thought the lanky hitman could be made available by the Reds if they fail to reach the knockout phase of the Champions League this season.