Koulibaly, 27, has consistently been linked with a move away from Napoli, where he arrived from Genk in 2014.
United are among a host of clubs to have been credited with an interest in the defender, as the centre-back continues to impress in Serie A.
And while the Senegal international said he appreciated the interest from other clubs, he claims to still have a high level of motivation to prove himself at Napoli.
"My future? I don't know if I'm one of the strongest defenders. I always try to give my best," Koulibaly told Rai Sport.
"Since I'm here, I always try to grow with Napoli. I have a lot of motivation to go on and I want to keep doing this.
"I am pleased that many teams follow me, but I want to demonstrate on the field that I am at the level of the greatest and I want to show it in the future."
Koulibaly has made 30 appearances in all competitions for Napoli this season, with the club currently sitting second in the league table.
The club are also alive and well in the Europa League, where they claimed a 3-1 win over Zurich in the first leg of their round-of-32 clash on Thursday.
Napoli will be hoping to hold onto their star centre-back, especially with the club having recently sold long-time hero Marek Hamsik to Chinese outfit Dalian Yifang.
It's unclear what United's transfer plans will be in the summer, given the uncertainty over who will be their long-term manager, although the signing of a centre-back would appear to be a priority.
Prior to Jose Mourinho's sacking, the Red Devils were seemingly keen on a deal for Harry Maguire, while there were also reports of interest in the likes of Diego Godin and Newcastle centre-back Jamaal Lascelles.