My gf has a housemate who will not leave her alone!!!

She spends quite a bit of time in the house with this guy, either watching tv or having a drink but they are never alone and always with other friends.

This guy has now started telling other housemates how he is in love with my gf which is now making me look weak for letting this guy disrespect our relationship.

She tells him that she is not interested and has a bf but he keeps on begging with her for "even a single date"!

I trust my gf 100% and i know she would never lie and all the trouble is from this guy.

What is the solution? Should my gf cut this guy from her life or should i bite his nose off???