Rehoming 2 month old Kitten

Hello I’m currently needing to rehome a stray I took in. I believe he’s about 2 months old. He was smaller when I found him but my dog can’t seem to accept him and will chase him down. I really need anyone’s help on taking him. I don’t want to give him up but my dog can’t seem to fathom the kitten. I’ve had my dog for 6 years and he’s my baby. I’ve had to kitten for about a month and nothing has changed. He has no fleas I’ve showered him and is litter boxed trained as well.