But the Scottish ace expects a tight battle until the final day of the season.
“We have still got a game in hand so we would like to think it is only five (points) so I don’t think it is (too big a gap),” Fletcher told Sky Sports News.
“I think there will be a lot of twists and turns. Liverpool have shown they are contenders and obviously Chelsea and Arsenal are.
“Teams are going to take points off each other. It is a very competitive Premier League and we feel we can go on a run of unbeaten games.”
He continued: “I don’t think these games (between the top four) decide titles. It is a long season and if we can be in contention after Christmas then we are notoriously good at the end of the season and we can really push on. That is our aim.
“We have got a lot of home games in the second half of the season and we feel confident playing at home with that sort of crowd behind us.
“Chelsea are obviously going to be there, Liverpool have shown promise and Arsenal are obviously a good side.
“The league went down to the final day of last season and I wouldn’t be surprised if it was the same again.”
