Rice is wanted by the Blues, even though he would cost the club a huge transfer fee.
But it is unclear if the 21-year-old is desperate to leave, as he is pleased with his football at the high flying Hammers this season.
Rice was asked by Sky Sports about the impact of leaving Chelsea for West Ham at the age of 14.
"I think that's the making of me to be honest with you," the England international replied.
"I had to move to West Ham at 14, away from my family. I'm a family boy, love my mum and dad, live at home with them, and to leave them at 14 to play with people I don't know from Monday to Friday, I think that shaped me into the person I am.
"I had to start being responsible for myself, but look, I've come here and flourished. I've had three managers that have really looked after me, I'm loving life here."
About playing in central midfield, Rice added: "I see this as my position, 100 per cent.
"I've played in midfield for the last three seasons and I think a lot of people get carried away with what they want me to do!
"My role is a holding midfielder and there's not really any flair in that. I'm disciplined, I make sure I'm always available for the team, I'm always in position, I get my passes off quick, I intercept and I tackle. I think a lot of people want to see things like step-overs and I've got that in the locker, but that's not my role!
"I can play at centre-half, but I've got much more to give and I think my confidence is growing in midfield. The more I start driving forward with the ball like I've done in recent games, the more I'll grow into that position.
"I watched the top players like Yaya Toure and Patrick Vieira and every time they see a bit of space, they'd drive into it and look powerful and strong and as a holding midfielder that's rare these days, so if I can keep adding that into my game, I can keep catching the eye.
"They, as well as [Roy] Keane and [Claude] Makelele, were wonderful footballers but they never overcomplicated things and knew what their games were and knew what their weaknesses were, and I do too.
"I think some fans are calling on social media for me to get the ball off Lukasz Fabianski and run the whole length of the pitch and score with the back of my head, but that's not my job!
"My job is to protect the team, have good positional awareness, get on the ball, keep it simple and keep it ticking.
"I know what my strengths are and what to base my game around."