Sullivan has stated that he was impressed with the performance of Randolph against Manchester United at the weekend.
The 29-year-old goalkeeper started the Premier League game at Old Trafford on Sunday evening and played for the entire 90 minutes.
The Hammers held United to a 1-1 draw, and Sullivan has praised the Republic of Ireland international for his display.
“It was a real team effort starting with Darren Randolph who once again showed his quality and produced an outstanding display,” the West Ham co-chairman wrote on West Ham’s official website.
“Darren has had to be patient but he has never moaned about the situation and showed his quality during the summer playing for the Republic of Ireland at the European Championship Finals.
“I was impressed by the effort from the whole team on Sunday but I thought Darren was the star performer.”
Randolph is West Ham’s second-choice goalkeeper, but the disappointing performances of Adrian have allowed him to feature twice in the Premier League this season.
The former Birmingham City goalkeeper did indeed play well against United, and he should retain his place in the Hammers’ starting lineup.
West Ham are 16th in the Premier League table at the moment with just 12 points from 13 matches.
Slaven Bilic’s side are only a point above the relegation zone and are still in real danger of getting relegated to the Championship at the end of the season.
The Hammers will take on United away from home at Old Trafford in the quarter-finals of the EFL Cup on Wednesday evening.