South Africa have reportedly threatened to pull out of their summer tour of England if Nasser Hussain's side refuse to play in Zimbabwe on Thursday.
Morgan is under pressure to send England to Zimbabwe
England have until 1400GMT on Monday to decide whether to play in Harare.
And United Cricket Board of South Africa president Percy Sonn is believed to have told his English counterpart David Morgan that South Africa might cancel their five-Test tour if they do not go.
England are still wavering after having their request to switch the game to South Africa turned down, both by the International Cricket Council technical committee and a South African constitutional court.
But the Daily Telegraph newspaper reported that Sonn, who sees the World Cup as belonging to the whole of Africa, increased the pressure by approaching Morgan during Saturday's opening ceremony.
South Africa are said to be willing to use recent reports of a terrorist threat in England to claim it would not be safe to tour.
The England and Wales Cricket Board is already facing the prospect of a huge compensation claim if it decides not to fulfil the fixture in Zimbabwe.
And the loss of a home series against South Africa could put it under even greater financial strain.