Chelsea's Israeli boss, whose position has become increasingly unstable after Monday's draw with Wigan, believes he has worked miracles to ensure Chelsea finish within touching distance of Manchester United.
"Realistically, we never had a chance from the moment I arrived because we were behind the leaders," he said.
"I think the pressure is on us but we've come from nowhere to fight for the title.
"I'm not even thinking about my future, even if I have a contract. If the club are happy with me then I'll continue. There's no issue.
"It's important that I do my job for Chelsea, nobody has told me I must deliver a trophy but I want to.
"In football anything can happen. I won't stop fighting until it's impossible to win and if United succeed then I'll be the first to congratulate them."
Grant has also promised to take action against defender Tal Ben Haim after the player criticised his manager by stating he would never have joined the club had he known that his compatriot would take over from Jose Mourinho.
He added: "The matter will be dealt with internally and if I think he was wrong we'll deal with it in our way. I need to talk to Tal and see what he has to say first."