The striker has been linked with AC Milan.
However, after the preseason friendly against Everton, Abraham said: "From the first day here in Rome, I wanted to demonstrate my passion for football and the desire to help the club. I am a smiling and always positive person. This is my first post-injury preparation, it is my season and I want to show that I'm back.
"The rumours, obviously, are nice, it means you're doing well, but I'm here with Roma and I'm available to do my best."
On the arrival of fellow striker Artem Dovbyk, Abraham added: "Ever since I was a child I have been used to competition and fighting for a place in the team. Dovbyk is strong and I welcomed him. We are two different players and, who knows, maybe one day Mister De Rossi will give us the chance to play together. If not, we will support each other."