Rice, though born in London, has only ever represented Ireland having declared four years ago through his Cork-based grandparents.
He recently turned 19 and his continued rise to prominence has made him a target for his homeland.
Martin O’Neill called him into the senior squad training week in Cork, just a couple of days on from his Premier League debut at Burnley.
But Rice’s performances, in particular the man-marking job he perfected on Tottenham’s Harry Kane earlier this month, have ensured Southgate and his coaches are interested in changing his mind about international allegiance.
There is no indication that Rice is disposed to following the example of Jack Grealish by defecting from Ireland, yet he will still be given that option.
Even if, as expected, O’Neill offers to hand the tyro a senior cap in the next friendly against Turkey on 23 March, the player could still jump ship. Players are not permanently tied to a country until they feature in a competitive fixture at senior level.
Southgate suggested he is comfortable allowing the English FA’s Technical Director Dan Ashworth to initiate contact with the Rice camp.
“We are aware of him and aware of his situation,” said Southgate, contracted as England boss until 2020.
“We are always looking for players and he is somebody whom we know. We are across every young player and, of course, there are plenty of young players with dual nationality. Wales have several players who have been in our system and who have got caps.
“It’s more a question for Dan Ashworth as technical director than for me as senior manager.”
O’Neill said: “Declan has done very well this season. We took him down for a little bit of training in Fota Island last year and he was an impressive young man I must admit.”
Meanwhile, Ryan Giggs admits he’s fully aware of Robbie Brady’s set-piece threat in the UEFA Nations League having seen it first-hand at Manchester United.
Although Brady is currently sidelined with a knee injury, he should be back fit in time for the trip to Cardiff on 6 September.
The Ireland attacker will come face to face with the Wales boss whom he developed alongside during his formative years at United. After just one first team outing, Brady moved on to Hull City and arrived to Burnley via a stint with Norwich City.