They have previously been in a relationship.
They know each other well and Natasha thanks Banner for saving her 'best friend'.
Many shippers claim the way that Clint talks to her and the way Natasha immediately helps once she's heard that Clint has been "compromised" are signals of their love. Loki, the villain, also appears to take interest in their relationship, saying, "Is this love, Agent Romanoff?"
Although Natasha denies it, many shippers say that Natasha is in denial. Also shippers have noticed that Natasha is wearing an arrow necklace in "Captain America, the Winter Soldier".
Many shippers were disappointed when Avengers: Age of Ultron revealed Clint was married. Nonetheless, the ship remains highly popular in the fandom.