England striker Abraham has scored 15 goals in 33 Serie A starts - and 24 goals in 46 appearances in all competitions - so far this season.
The 24-year-old left Chelsea last summer to join the Giallorossi in a £34million transfer on a five-year contract, having ended the previous campaign as the Blues' joint-top goalscorer.
The high-profile move saw Abraham link up with former Chelsea manager Jose Mourinho in the Italian capital.
However, the striker, who had loan spells at Bristol City, Swansea City and Aston Villa before leaving Stamford Bridge last summer, says he is relaxed about the speculation.
Speaking ahead of Thursday's Europa Conference League semi-final first-leg trip to King Power Stadium to take on Leicester City, he told reporters: "I'm happy playing my football. You hear the little rumours here and there but clearly I'm doing the right thing. I give credit to my team-mates, the staff and manager.
"I was born and raised in England, of course there are many rumours here and there that there are clubs interested but I'm clearly doing something right at Roma if people are interested.
"I have to stay focused, keep doing my thing and I'm happy playing my football."
Thursday's first-leg clash at King Power Stadium marks manager Mourinho's first game back in England since he was sacked by Tottenham last April - after just 17 months in charge.
Mourinho said Roma, currently fifth in Italy's Serie A - 16 points adrift of leaders AC Milan, can expect a tough night against Brendan Rodgers' Foxes.
He told reporters: "I think that, based on the hard work we've put in this season to improve and to get to this stage, we deserve to reach the final. Sometimes football rewards that hard work, but we have to face a great side.
"We have to be at a high level in two matches to reach the dream of taking Roma to a final."