The Daily Star reports that Allardyce is considering making a move to sign the striker on loan for this season.
Allardyce has spent almost £22million on Andy Carroll and Stewart Downing from Liverpool and would prefer to bring in another striker on loan.
Ba insisted last month that he has no plan of leaving Chelsea this summer.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?