Hayward enjoyed a successful first season with the County, taking 67 wickets as they gained promotion to Division One of the County Championship.
But the South African had not confirmed he would be returning to Worcestershire for a second campaign, and now the county are stepping up their efforts to get Bichel.
The Australian was a popular and successful character during the 2001 and 2002 seasons with Worcestershire and also made several important contributions with the bat.
"There was a one year option on Nantie's contract that we wanted to take up," Worcestershire chief executive Mark Newton said.
"He did a good job for us in 2003 and on the field he made a sizeable contribution in a successful season in the County Championship.
"But he did not confirm officially to us that he would be coming back to Worcestershire for 2004 and so we are looking elsewhere."
Newton would not confirm Worcestershire's interest in bringing back Bichel, but admitted: "As a club we have maintained regular contact with Andy since his two years with us in 2001 and 2002. We have always been aware of his situation and there was always a feeling between him and ourselves that it would be lovely for him to come back sometime in the future."
Bichel is also a target for Warwickshire after they lost out on acquiring the services of Darren Gough to Essex.
Andy Bichel makes way for Kasprowicz