The Hammers are believed to be keen on landing Bacca as manager Slaven Bilic seeks a new striker.
Co-owner David Sullivan has already pledged £30m from West Ham's transfer budget is available to spend on a goalscorer.
And negotiations are supposedly underway between the two clubs after West Ham launched an opening bid of £21m.
Bacca, 29, only joined Milan from Spanish side Sevilla last summer but the Serie A club are already seeking a buyer.
Financial problems at Milan - Silvio Berlusconi is still looking to sell his stake in the club two years after putting it up for sale - mean they may be forced to sell their star players this summer.
And West Ham, whose bid includes £4.2m in add-ons and bonuses, are ready to offer Bacca an £80,000-a-week contract.
GETTY
Colombia international Carlos Bacca could join West Ham
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Liverpool's Most Expensive Transfers
Christian Benteke is not close to joining Crystal Palace, the Liverpool striker's agent insists.
Reports emerged at the weekend claiming Benteke, 25, had agreed personal terms with the Eagles ahead of a move.
All that was to negotiate, it was thought, was the transfer fee.
Liverpool paid £32.5m for Benteke a year ago and supposedly want £32m this summer.
But his agent Kismet Eris has told Sky Sports there is "nothing in" claims that Benteke is set to quit Anfield.
The Belgium international scored just 10 goals for the Reds last season.