Tenant wants a change in Tenancy Agreement

(Assuming standard English assured shorthold tenancy)

(I am aware I have to let them stay for a min of 6 months).

There are no minimum contract length.

When the current fixed term ends, a statutory periodic tenancy will automatically arise by automatic operation of the law if the tenant doesn't leave. Neither you nor the tenant have to do anything for that to happen, and you cannot prevent it from happening. Only the tenant can, by leaving by the time the fixed term ends.

It's generally inadvisible to agree contract with new tenant before existing tenant leaves and you have possession. If for whatever reasons they refuse to leave, you'll take time evicting them. Or you don't know if you need to do any works to refurb etc. Then you're in trouble with new tenant being unable to give them possession. Minimum void is nice, the risk however is not necessarily worth it.

Can I ask if you think this is reasonable or if you are aware of a better way to handle it?

It's not reasonable and you are trying to circumvent a Tenant's statutory rights... not by design, I'm sure... but that is the effect.

They have an agreement that is coming to an end.
You cannot force a new fixed term agreement on them... you can try, and if they don't agree you can start eviction proceedings (which would take ages and cost).
If you do nothing at all and they remain there - a SPT automatically arises.
In that scenario you have to give them at least 2 months notice.
And they have to give you at least 1 month notice (you cannot override this by any agreement you might come up with - except one of honour and good nature, on their part, I suppose).

That is the way it should be. Sometimes you just don't get the security you, ideally, want. One of the pitfalls of the PRS.

The Tenant appears to be quite reasonable / helpful... asking for a three month agreement seems to imply they're either unaware they can go to SPT by doing nothing at all or are trying to assist your worries. I can't read more into it, of course.

The Tenants holds most of the cards here - you have to accept that and hopefully keep a good working relationship for the remainder of the time they're there.

Personally... I never even put my properties on the market until they are empty of the last Tenant. Maybe I am very inefficient in this approach... but only once have I been tempted into letting viewings happen while an existing Tenant was there... no-one involved liked the experience, that much is certain.