Sinclair has revitalised his career at Celtic since his move from Aston Villa in the summer of 2016 for a transfer fee reported by The Guardian to be worth £3 million.
The former Chelsea and Manchester City man was a key player in Celtic’s Scottish Premiership triumph last season.
Southgate, though, has not included Sinclair in his England squad for upcoming World Cup qualifiers against Slovenia and Lithuania.
The 47-year-old, who has Premier League managerial experience with Middlesbrough, has explained why he did not 28-year-old in his team.
The former Crystal Palace and Aston Villa man has also revealed that he had a conversation with Celtic manager Brendan Rodgers about Sinclair at the end of last season.
“I had a conversation with Brendan [Rodgers] about him at the end of last season," Southgate told The Glasgow Evening Times.
"He's a good player but we have good quality in that area of the pitch and at the moment I think he is just below the level of what we have already got.
"I would be happy to have that conversation (what he needs to do to break through) with him but I don't think it's appropriate to talk about performance aspects in public."