Hart has been England's number one goalkeeper since Euro 2012 and retained the role even after he moved to Torino on loan last season, having been deemed surplus to requirements by Manchester City manager Pep Guardiola.
The 30-year-old returned to the Premier League in the summer but has already conceded 30 goals in 14 league appearances for the Hammers, keeping only three clean sheets in the process. While West Ham's calamitous defending has played a role in the number of goals Hart has conceded, the ex-Shrewsbury Town stopper has only shown glimpses of the form that made him a regular at City for six seasons.
And Southgate has admitted that Hart's lacklustre form, coupled with the emergence of Everton stopped Jordan Pickford and Stoke City's Jack Butland, means the West Ham goalkeeper cannot rest on his laurels.
"Joe has been our number one through the qualifying campaign and has performed really well," the England manager was quoted as saying by Sky Sports.
"We know there is great competition for places. Three types of goalkeeper in as many ways - in terms of their experiences and styles. Plus we have the likes of Fraser Forster and Tom Heaton, who is out injured, and there are other young goalkeepers coming through."
England qualified for the World Cup in Russia with an unbeaten record and kept clean sheets against Germany and Brazil in back-to-back friendlies last month, which Southgate cited as proof of his side's defensive solidity.
"We had the best defensive record in Europe," he added.
"We have also come off the back of two nil-nils against Brazil and Germany so in terms of our defence and our goalkeepers they have had as good performances as anybody in Europe up to this point.
"If we play tomorrow, I think Joe Hart would be our number one. I said that before the last game and he had a very good performance against Brazil. Equally, as I keep having to say to him, we are six months away and he has got to maintain form and make sure [of that] in the lead up to the World Cup."
England will find out their opponents for the group stage of next summer's World Cup on Friday (1 December), with the draw set to get underway at 3pm GMT. Southgate's men will be placed in pot two for the draw and will be hoping to avoid some of the heavyweights in pot one, which includes Brazil, Germany, France, Argentina and Portugal.