The £35million striker was offered to Manchester City in a swap deal with Carlos Tevez.
Andy Carroll: "I'm not bothered by speculation.
"Not at all.
"The club has been great with me and everyone outside the club has been fantastic and I am enjoying it down here.
"Everyone has backed me and helped us along the way. I have signed a contract here and this is the team I am playing for.
"I thought I did well against Manchester United but I've got to keep working on it and it will come.
"I am just getting into my stride now. Everyone is getting used to how I play and I am getting used to everyone else.
"Everyone is helping us as much as they can and I just need to get going."