Best friend's widower's new partner

Imo, you need to meet a few times before there's any talk of anyone staying with anybody. And if they do stay over at any time, it needs to be a short visit. Just don't invite them to stay, right now, and if friend's widower asks make your excuses. Or, if you feel comfortable, let him know you want to take time to get to know his new lady first.

He needs to be realistic, imo. This isn't the same as when you all lived together, etc. There's a new person involved and time is needed to nurture a new relationship (if that's what everybody wants). He needs to think of her, too. Most likely, an extended visit with her new man's deceased wife's friends would be very uncomfortable for her. "Forcing" a relationship isn't going to work for anyone - don't let him try it.

Of course it is for the living , but I wouldn't fancy a stranger staying in my house, all the OP has in common with the Man is his deceased Wife

This man (your friend) has been a widower for three years. Life is for the living. I'd extend a warm welcome.

Men don't get their brain in gear ! meeting the lady for a meal would be a better option

Yes, staying with you, even just overnight, seems too much too soon. A meal at a half-way point is a very sensible suggestion.

Suggest you meet them for a meal somewhere first and get to know her. Can you meet somewhere halfway if they live a distance away?
You may be surprised, you could get on really well with her.

You don't say how long they would be staying , if it's just one or two nights that shouldn't be too bad, and would give you chance to see if you would get on together , then you would be better prepared should he suggest it again in the future

I think that staying with you is a bit much....for all concerned.Go out for a meal together.

I see no problem in meeting his new partner, but why do they need to stay with you? I would just meet for lunch to get to know her.

Welcome her with a positive mindset - it is lovely that he wants to bring her to see you.

I'm not sure she wants to meet me, he has just suggested that he might like to bring her to stay. I am happy for them both, but it just feels a bit weird.

One of my dear friends died 20+ years ago and when her H eventually remarried, his wife wouldn't meet us,
I think she was worried about our reaction. We were actually dismayed as was our male friend, so you really should be very happy that she wants to meet you and so does he.
When our friend died his wife rang to tell me as she knew how close we all had been.
Since then we have rung and e-mailed each other a couple of times a year although we have never met.
It still strikes me as a rather strange affair.