The Reds will include out-of-favour striker Rickie Lambert as a sweetener in a deal to land the DR Congo, who was recently valued at £20m by Eagles boss Alan Pardew.
Bolasie, aged 25, has been in sensational form in recent week. He had previously been linked with a move to Anfield last summer and the extra gear he has found recently is not likely to have done anything to deter the Reds’ interest.
Liverpool value England international Lambert, aged 33, at £5m, which means they reckon their offer to Palace will be worth a total of £15m.
He joined his boyhood club from Southampton in a £4m deal last summer but has failed to secure regular starts since his move to Anfield. It was Pardew who originally signed Lambert from Bristol Rovers for the Saints.
Bolasie arrived at Selhurst Park from Bristol City in 2012.