The Wanderers offer is more than Everton were willing to pay as they need to hold back some cash to fund a new striker.
Bolton and Everton are also lifted by news that Real Madrid are only willing to offer £25,000-a-week to Keane for six months. The Premiership rivals expect an answer in the next 72 hours.
Allardyce said, "We're still talking to his representatives in terms of what the financial situation would be," he said. "We'll see what decision Roy makes after that.
"I have spoken to Roy, but not round the table. I think it now lies with the chairman speaking to his representatives and seeing where we go."
"There are other players too," he said. "Our main aim is that this squad is good enough, big enough and strong enough to carry us forward into January and until the African Nations Cup players go away."