Guys, Is my coworker being inappropriate?

[Anonymous]

He is very shy; and when i first started, he would reach out to me & ask how i'm doing every couple of days. We met in person (our offices are in diff countries) & he didn't talk to me at ALL. But as soon as i was home, he msged me "sorry if i was really introverted" - & now we have regular off-topic convos late at night- 10 pm ish & he always keeps the convo going. Is that considered inappropriate?

Updates

10 mo

Does it mean he's attracted to me?

[LiamS95]

Only if you feel it's inappropriate, he has mentioned and apologized for being very introverted

[Knightwatch27]

I really feel like a woman your age should be capable of deciding that on your own.

[nl171]

If it doesn’t make you uncomfortable then I don’t believe it’s inappropriate

[Avicenna]

Not if you’re ok with it

[In_Trance]

No more or less than you are