A source said that the singer rejected the drink after she realised that it was prepared in tap water.
"She was offered a cup of coffee by one of the staff," News of the World quoted a visitor to the London Chest Hospital, as saying.
"But he wanted to know what kind of water had it been made with—bottled or tap. Obviously it was tap water and she said, 'No, thank you'.
"The staff were bemused. Water is boiled anyway, so people didn't understand what the problem was,' the source added.
Another source said that Posh Spice wanted to redo her make-up and changed outfits between two visits to the hospital, where Ted Beckham was recuperating from a heart attack.
"On another occasion Posh wanted to redo her make-up," another source revealed.
"She asked one of the cleaners if there was somewhere she could go. In the end she used a staff room in the high dependency unit.
"She and David came back at about 11pm for a second visit, and by then she'd changed outfits,' the source added.
The source also said that her hubby David Beckhams chatted with other patients and staff at the hospital, but the pop singer preferred give all a frosty-nosed look.
"She has that fixed pout. You didn't know if she was going to kiss you, talk to you or ignore you,' the source said.