This guy may keep looking at you in this way because he is attracted to you.
The thing is, he may also be really shy. Hence, you may catch him constantly looking at you but not making a move.
He may be entertaining certain thoughts that could start getting out of hand if he is unable to keep them under control.
In his mind, he may be wondering what it would be like if he were to make a move on you and possibly ask you out or start a conversation.
He may be worried that you will reject him or won’t be too welcoming to his approach.
This could be a major reason why he just keeps looking but doesn’t approach.
He may also be assuming that you already have a boyfriend.
A lot of shy guys do this.
They see a girl that they like and immediately make the assumption that this girl most certainly has a boyfriend.
She is way too attractive to be single.
The shy guy allows himself to think in this way until he talks himself out of actually approaching her.
He tries to make himself feel better by telling himself that it would have been pointless anyway because the girl is taken.
However, somewhere in the back of his mind, he knows that the real reason why he didn’t approach this girl was because of fear.
He may not want to admit it to himself but he is simply afraid that if he were to approach her, she would simply turn him down.
He can’t bear to think of how that would make him feel, so he plays it safe.
If all he did was to simply look at you, he hasn’t committed to anything.
He hasn’t taken any kind of risk.
He can essentially fill in the blanks as far as what he is fantasizing about.
He may see the both of you doing romantic things together in his fantasies.
He can let those fantasies take him away for a moment. He gets lost in them.
When he comes back to reality he feels that it would be better for him to maintain a fantasy about you than to take the chance of getting turned down by you.
There are also some guys who keep looking at you because you may remind them of someone.
You may actually remind them of a past love or romantic interest.
In those moments that they are looking at you, they may be reminiscing about that person.
Their thoughts may be positive due to fond memories of this person or they may be negative.
They may begin to wonder what that person is doing now.
They may even question how they behaved and whether they lost out on an opportunity with this person in their past.
In essence, your presence is triggering memories that may be causing profound emotions in them.
As they get deeper into their recollection of this person, they continue looking at you.
They may not even necessarily realize that they have been looking at you for quite a while because they may be lost in thought.
They may appear to be almost in a trance-like state at that moment.
When they see that you have noticed them, they may snap out of it.
However, still curious about those memories and who you remind them of, they may return their gaze once more only moments after.
They just can’t help themselves as they are continually drawn to the source of what has caused these memories to come about.
The effect could persist even after you are gone.
They just keep recollecting a past memory and perhaps they either regret or appreciate certain elements of it.
However, something has been triggered and they may find it difficult to get you out of their mind for the rest of the day.