Neill left Upton Park when his contract expired at the end of June.
“Lucas is not going to accept any offer,” Dominguez told The World Game. “Lucas’ heart is at West Ham and he knows that manager Gianfranco Zola not only wants him at the club but also as captain.
“So now it is up to the West Ham administration to come up with an acceptable offer for an extension of his contract.
“We are not talking about a new contract here but an extension, which would be easier for everybody concerned. We should have something in about a week.
“It has always been the preference of Lucas that he wants to remain at West Ham. But it is up to the club administration to execute that.
“The ownership has changed a number of times since Lucas has been at the club. Now it’s different because they [the owners] are bankers.
“We are giving them every opportunity to reach agreement but there are other EPL and continental clubs in the mix.”