The Premier League giants are the latest club to formally enter the race, according to reports from the Italian press on Monday.
Their arrival has added fuel to what is already being described as a bidding war reaching "unprecedented heights", with Liverpool and Tottenham Hotspur also firmly in contention.
Roma, however, are reluctant sellers and are understood to value Ndicka at around 45 million euros (39m GBP), viewing him as a prized asset.
Ndicka, an Ivory Coast international, has earned widespread praise for his performances in Serie A, where he is now regarded as one of the division's standout defenders.
European football expert Andy Brassell has endorsed the 24-year-old, suggesting he would make a significant impact at Old Trafford should United secure his signature.
"I think he's one of the very best central defenders in Europe, and I don't think he's ever really given credit for it," he said on talkSPORT.
"If I was a Premier League club, I would be all over Roma for Evan Ndicka. I think he's already a great defender, and I think he'll get even better."
The defender's rise has been steady. Born in Paris, Ndicka came through the ranks at AJ Auxerre, making 16 senior appearances before securing a 5.5-million-euro move to Eintracht Frankfurt in July 2018.
During his time in Germany, he made 183 appearances and scored 12 goals, playing a crucial role in Frankfurt's Europa League triumph in 2022.
After leaving Frankfurt on a free transfer in 2023, Ndicka joined Roma, where his reputation has only strengthened.
