The second structure is the correct one in this case.
'interested in' doing something talks about hobbies and topics which you enjoy learning about in general, for example:
I am interested in French poetry
I am interested in dancing
It is also used to talk about things which you would like to do:
I am interested in joining your reading group
'interested to' is only used with certain verbs - see, hear, find out, learn - and it is usually used to say that you would like to find out more about a topic, or alternatively that you are even quite surprised about something:
I was interested to find out that Ronaldo grew up in a poor area
I was interested to see the culture in India
In your sentence, you would have to use 'interested to', because you are talking about the fact that you may want to hear more about the fact that someone's English has improved.
I hope this helps!