Southgate last month outlined his desire for a creative midfielder in the mould of Paul Gascoigne, something which might have attracted Barkley's attention given prior comparisons made between the two players.
"I was getting used to that role as a first-team player but usually I was a No 8 or, before I broke my leg, I was a deep-lying midfield player".
Six of Chelsea's last nine Premier League goals have been scored by the Belgian worldwide, who also bagged a sensational victor in last week's Carabao Cup success at Liverpool. I don't know how many we have to change, but we have to change.
Barkley, whose career has been disrupted by injury, has not played for England since May 2016 but said his performances for Chelsea this season proved he was ready for a return to the national team.
Sarri said: "To play in the Champions League is more important at the moment (but) I want to arrive in the end in the Europa League".
Cesar Azpilicueta had been wearing the armband on the pitch in absence of Gary Cahill so it makes ideal sense to make him the new captain.
"I think so, because he is improving week by week", Sarri said when asked about Barkley's worldwide chances. "I hope we can do better [next] time".
Pedro and Ruben Loftus-Cheek have had difficultties in recent weeks with injuries, but they should be avliable for selection regardless.
The Hungarians have not had a good start to the season as they now sit in third place in the local league, eight points behind the leaders, and losing their first Europa League group stage match 2-0 to BATE Borisov. "I hope to be able to do it".
Chelsea dropped points in the Premier League for the first time this season after their win over PAOK, as they were held to a 0-0 draw by West Ham three days later.
"I think that he can improve more, because he has the potential to".