Chelsea's strikers will love playing with Juan Cuadrado if he does join, says Thierry Henry.
Manchester United boss Louis van Gaal has said that Darren Fletcher's proposed move to West Ham is off.
The 25-year-old had one year left on his previous deal but his extended contract will now keep him at Turf Moor until the summer of 2017.
"I'm delighted to have extended my deal with the club as this is where I want to be playing my football under this management,” he said.
"We had a great year last season and this is a club is going in the right direction so I'm made up to be a part of that.
"I felt like I was getting back to my best last season and a massive factor behind that was because I was enjoying my football and I felt I could go out and express myself.
"We've got a great bunch of lads and there is a real togetherness in the squad, with everyone pulling in the same direction.
"Obviously it is going to be a tough season ahead but if we stick together and work as hard as we did last year then I think we can have a successful season."
Scotsman Arfield began his career at Falkirk before joining Huddersfield for an undisclosed fee in the summer of 2010.
Burnley signed him on a free transfer last summer and he made 49 appearances in all competitions for Sean Dyche's side, scoring nine goals to help them secure promotion from the Championship.