Manchester United, Celtic, Stoke, West Ham, Arsenal and Tottenham have also been credited with an interest in Barton.
Whelan has confirmed he will make the funds available to manager Roberto Martinez he feels the midfielder would fit in at the DW Stadium.
Whelan: "I would say 'Roberto, I'm backing you'. He's the boss and I let him be the boss. If Roberto would like to sign Barton, I'd try to get him."
The Latics are likely to face plenty of competition for the midfielder with Stoke and Aston Villa also tipped to make a move, while Barton's agent Willie McKay has previously indicated there is interest from European sides as well as domestically.