Chelsea starlet Abraham, who has scored four goals in his last two Premier League games, hit 26 while on loan at Aston Villa last season, helping them to promotion to the top flight.
The 21 year old has already played for England at Under 18, 19 and 21 levels, and has made two appearances for the senior team in friendly matches against Germany and Brazil in 2017.
But Nigeria, who he qualifies to play for through his father, have made attempts to poach the Chelsea youngster.
Nigeria Football Federation president Melvin Amaju Pinnick stated earlier this month that Abraham would have a better chance of getting games with his country than with Southgate.
But Abraham has told friends that he has no intention of switching his allegiance from England.
Southgate said: “Tammy is a young player that we’ve always liked, we know he’ll score goals. We felt it was a bit early this time to call him up, but we really can see that he can offer us something moving forward.
“We gave him a cap back in November of 2017.
“For sure, we need to make certain that he feels that the opportunity is going to be there. I’m pretty sure he does, he knows us well enough.”
As for a possible return to the international fold for Leicester striker Jamie Vardy – who told Southgate in August last year he did not want to be considered for selection unless there was an injury crisis – the England coach was less welcoming.
A revitalised Vardy, 32, has netted three goals this season, but Southgate said: “It’s obvious how well he’s still playing, and the discussion we had at the time was: “Neither of us close the door.” There’s no point in him travelling if he wasn’t going to be starting at his age. I can understand that.
“We wanted to look at developing younger players. I wouldn’t see the point in bringing him back in immediately, but the door isn’t closed because he’s still a top player and scoring important goals in big matches. And he’s a character we’ve liked having around.”