Hamilton has been linked with various possible moves away from McLaren, including to Ferrari, but Neale has said he is likely to stay on for at least another season. He also believes the Englishman can still win the drivers' championship despite being 47 points adrift of Fernando Alonso.
Neale said both McLaren and Hamilton were hopeful of reaching an agreement. "We are closer and of course we are in dialogue," he told Sky Sports. "For obvious reasons I can't speculate more at the moment. We are working very hard to find a common ground."
Hamilton is fourth behind Alonso but Neale believes that, with nine races to go, there is still enough time to chase down the Ferrari driver.
"Mathematically it is still possible with 25 points for a win and it doesn't take much to switch those," he said. "We have a quick car. It was in better shape than Ferrari at the last race. Lewis is a fighter, he loves a challenge. He just needs a sniff of it and to feel that the team is behind him and pushing.
"And I think that, if he feels we are pushing and bringing in the upgrades and dealing with the issues as they arise, then he will be fighting for the title at the end of the season."
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