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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.