Saitama and Tatsumaki don't have a particularly romantic connection. However, their interactions were amusing and entertaining enough for the audience to ship them. At the same time, it is safe to say that there is no possibility of the Saitama and Tatsumaki fanship turning canon.
As for the manga, till One Punch man chapter 175, Fubuki is shown to have harbored no romantic feelings for Saitama. She does have an odd relationship with him, given how she occasionally shows up at his home with other acquaintances.
In One-Punch Man's case, the tone of the manga and Saitama's oblivious attitude make it very unlikely that the protagonist will ever end up in an actual romance. The Psychic Sisters Arc, however, plays with these elements to tease a hilarious love triangle between Saitama, Fubuki, and Tatsumaki.
Saitama's Potential for a Love Life in One-Punch Man
He has been slowly rejoining the world and has developed more relationships through the course of the series, but he is still far too detached from his own emotions and has shown little desire for companionship, much less a romantic partnership.
Now, readers learned that not only Saitama is capable of suffering, but he is also afraid of completely losing his humanity, and this is why he kept close to friends like Genos, King, and even Bang, despite his apparent annoyance towards them.
Like, Saitama clearly never derives pleasure from anything other than doing his hobbies or fighting strong people. He never seem to have any sort of interest in the opposite sex, nor his own sex.
There is clear evidence that the Tornado of Terror, Tatsumaki, has romantic feelings toward the protagonist of the series. So far, there isn't any interaction that could even remotely show any romantic interest between the two.
Saitama is a bald-headed 25-year-old man who is bored of fighting because he is able to effortlessly defeat enemies with a single punch. He lives in an apartment in City Z.
Saitama is an ordinary-looking bald man with brown eyes, a thin but well-built physique, and is of average height and weight. He used to have a full head of short black hair but lost it due to the intensity of his hero training regimen.
Fubuki is a fox-girl; specifically an arctic fox. Prior to joining hololive, she lived as a mountain fox, and spent a lot of time sleeping. Japanese foxes are capable of assuming alternate forms, and Fubuki took hololive as an opportunity to spend time living as a human.
While Genos was supposed to be male, Murata did draw him as a female!
The big reveal is that when Saitama finally meets him, he will put two and two together and find out that Blast is his dad. Yes, he is supposed to be an elusive character, but especially with the other stuff we know about him, this just makes sense. The writers are still setting up their fateful meeting.
All of this proves very true when Saitama unknowingly amasses a harem of ladies through his interactions with them with delightfully chaotic results.
Psychic Resistance: Golden Sperm is able to very effectively resist an injured Tatsumaki's psychic attacks with apparent very little effort. However, it has been confirmed that if she was in perfect condition, he could lose.
Saitama, also known by his hero name Caped Baldy, and also as One Punch Man, is the titular protagonist of the webcomic/manga/anime series One Punch-Man, and the most powerful known being in the series.
To sum things up, Saitama hasn't received a promotion to S-class as of chapter 164, but it is very likely for him to receive one after defeating a considerable amount of strong characters.
I don't see it happening anywhere in the foreseeable future. Saitama sees Fubuki as more of an annoying acquaintance (in the webcomic he specifically says that she isn't his friend), and Fubuki is constantly advertising her B-class gang to Saitama and all of the S-class heroes he hangs out with (Genos, King, Bang).
For Tatsumaki, instead, her power is the result of a cold, relentless attitude that made her discard personal relations to become as strong as possible on her own. However, Tatsumaki's hard-as-steel shell has just been broken by the most unexpected of Saitama's attacks: a hug.
tatsumaki gets a crush on saitama.
After the Monster Association's downfall, Black Sperm becomes Saitama's pet, alongside Overgrown Rover. Black Sperm and Overgrown Rover are currently under the watch of Forte, Chain'n'toad, and Butterfly DX.
The metaphor of defeating everything in one punch and searching for the fight that will fulfill him is Saitama's way of living with not only his shortcomings before he became a hero but also his loneliness and depression.
After saving the life of a young kid, he decided to become a hero. In that endeavor, Saitama wanted to improve his endurance and strength. He persisted with a mind-boggling routine of 100 pushups, 100 sit ups, 100 squats and 10 kilometers of running. Apparently, this workout regime is the reason why he went bald.