What's going on here?

[Pricklypear12]

There's a male cat (looks like he isn't neutered) that has been hanging around my garden and door and kitchen window for many days. He seems to be pursuing my own female cat (neutered, about 3 years old). He doesn't show aggression but seems really desperate (gently meows towards her) to get close to her and she just trots off not particularly bothered or like she's avoiding him. What's going on here? Is he trying to mate with her? I thought as she's neutered (and has been since she was a kitten) that she wouldn't attract males?

He looks quite stocky so I don't think he's after food and I've put a bit of cat milk outside but he's not overly fussed.

He did manage to get inside to try get close to my cat today and she didn't seem overly fussed but did hiss at him so I managed to gently shoo him out as he seemed keen to get close to her.

Can anyone shed some light?

Thanks in advance.

He's trying to make overtures in the hope of getting his furry knee down. Obviously she isn't having any of it.

Our spayed girls would still attract attention.

Unneutered males will go after anything

We are bothered 4-5 times a week by our local unneutered tom as he walks down the road howling on the off chance he's in luck. He also sprays all over the back door and tries to come in through the cat flap although that might just be for food as for two very different reasons none of our cats are interested in him.

Thanks all! He's probably just trying to get a paw in then!