The Portuguese boss will look to make it two north London derby wins in a row when the Gunners visit on Sunday.
They boast the best defensive record in the league after conceding just nine goals, with Hugo Lloris contributing four clean sheets to the record.
While the Frenchman has played all league games, he has been excluded from the Europa League campaign for the last three games.
Hart was between the posts for the most recent game, a 3-3 draw against LASK, to make it six appearances for the season.
But football.London have reported that Mourinho may need to rely on the Englishman again sooner rather than later.
Lloris did not travel to Austria for the Europa League clash, hainv missed the Ludogorets trip over illness before coming back in the 0-0 draw against Chelsea.
Spurs, though, have not confirmed if the shot-stopper is carrying an injury – but the report states there is “understood to be uncertainty” over his availability for Arsenal.
If Hart is selected ahead of Lloris for the north London derby, it would give the Englishman his first league appearance since Boxing Day 2018.
Spurs have not lost to their rivals since December 2018, recording two wins and two draws against the Gunners.
Asked if the Portuguese manager agreed with Eric Dier’s statement that the Spaniard is “the most exciting young manager in Europe”, the boss said: “I don't want to go in that direction because I don't know them all, and it's very hard to say that.
“I think Mikel is a good coach, but I want to respect the others, especially the others that I don't know well, and probably are also very talented.”