Abraham is in his first season in the Italian capital and has put up some impressive numbers in front of goal.
The 24-year-old has made 41 appearances across all competitions so far this season, scoring 23 goals.
Abraham joined Roma from Chelsea on a five-year contract worth £34m at the start of the season.
Talking to talkSPORT, Abraham said: 'For me I’ve always been a player growing up, watching the Premier League and watching football.
'When I heard about different teams and certain players I always thought: Wow I want that to be me one day.
'I’m sitting in bed one day on Instagram that Tammy’s been linked with so and so and as a player it makes you feel good.
'As a player it makes you feel like you’re doing something right. For me it’s a nice feeling to be linked. To see your name all over the newspapers etc.
'But for me it’s just doing my business here. Focusing on what I am doing here so I can keep getting linked with all the clubs.'
Chelsea included a buy-back option in Abraham’s contract with Roma which comes into effect in the summer of 2023 for £68m and the England international has not ruled out the prospect of retracing his steps.
'It’s all over the place at the moment. Who knows what the future holds," Abraham added.
'Of course I grew up in England and I’m a London boy so maybe one day I will be back in the Premier League to make noise there.
'But, for me right now, it’s about focusing in Rome. It’s about focusing on doing the best I can and hopefully I can win these guys a trophy, which they haven’t won in many years.'
