Burnley manager Stan Ternent told the club's official site: "Whether the offer is acceptable or not, I'm not quite sure but the financial situation may dictate what happens."
The fee is rumoured to be between £300,000-500,000 with a Forest player moving the other way.
David Johnson, who spent some time on loan at Turf Moor, is believed to have recommended the Welsh international to Paul Hart.
Johnson made a public outburst following the Reds' 3-0 defeat at Reading last week saying Forest were acting like a club 'in administration' after not strengthening throughout the summer.
Taylor would add power and competition for places upfront with only Harewood and Johnson the current senior established strikers.