With Natasha Romanoff's last outing coming up in The Falcon and the Winter Soldier, and Yelena ing the MCU in Black Widow, the spotlight is on the two characters, and they have a great deal in common. With Natasha and Yelena both being a part of the Red Room experiment by the Soviets, and Barnes a former Soviet/HYDRA experiment, they share some considerable history that they're trying to move beyond.
The comics told a story of romance between the Winter Soldier and the Black Widow, which was significantly more successful than the MCU's attempt at romance between Natasha and Bruce Banner. Natasha's knowledge of the Avengers: Endgame, meaning that both she and Bucky could come into a healthy relationship as equals.
While Bucky's path toward wellness took him out of commission following Civil War, and his disappearance following the Snap removed him from circulation for another five years, his role in the miniseries with the Falcon means that he is back in action. This may include an effort to build more normal relationships, traditionally hard for superheroes. The effort to force a romance between Black Widow and the Hulk felt stilted because they had little in common, and no chemistry. Although brainwashed into an emotionless mask by HYDRA, Barnes was originally a tremendous flirt, and his ability to both defend himself and relate to the difficulties of another recovering former assassin could help him relate to Yelena.
The fact that Barnes and Romanoff were an item in the comics doesn't mean a lot - the MCU has proven time and again its willingness to diverge from the comics, a willingness necessary when adapting such an enormous body of work. As a primarily martial hero, Barnes is augmented, but not a super-scientist or sorcerer, giving him an even footing with a similarly trained and enhanced Black Widow. Neither likely has a great deal of exposure to modern Western media, giving them a shared media catalog to explore. While Bucky looks to be cured of HYDRA programming, having someone capable of looking out for themselves around him would likely help him to be at ease.
Whether Barnes and Belova end up in a relationship or not, they do share enough common ground to become good friends and allies when they meet one another. As was evidenced by Hulk and Black Widow, making a romance click in a film or TV show can depend a lot on on-screen chemistry, and while both Sebastian Stan and Florence Pugh are talented actors, time will have to tell. Nevertheless, both characters deserve a break and a shot at finding happiness, having been through quite a lot, and Phase 4 can atone for missing out on their opportunity to have a similar relationship between Barnes and Romanoff. How practical such a story ends up being will depend a lot on the story of Black Widow.
