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The player's agent, Neil Fewings, has hinted that the talks could well drag on into August but Megson wants the matter to be settled sooner rather than later.
The boss does not want the question mark over Hughes's future to be allowed to continue, especially as he knows that if Hughes does snub the deal, he will have to find a new striker as Albion will have no option but to sell the 25-year-old flame-haired marksman.
Megson said: "It would help both parties if Lee could make a decision sooner rather than later. It is a grey area that needs to be cleared up."
Albion are continuing to stay tight-lipped over speculation that Hughes has a clause in his contract allowing him to leave if a club should offer £5million.
That is only £500,000 more than Birmingham have hinted they are willing to offer for Hughes, who remains a City target despite their earlier capture of Tommy Mooney.
Birmingham's main problem, if Hughes should snub Albion's offer, is that he is likely to be keen to move straight into the Premiership rather than swap Albion for another First Division side - especially a side who are one of Albion's local rivals.