How to formulate a bid for a property?

This is not a public auction. He can at any time claim to you that there is a higher bid (even though that might not be the case) to drive up the price. That's how I would do it ;)

Make an offer that is acceptable to you as the maximum amount and that's it.

It always depends on how personal the contact is, how many bidders there are, and whether one can somehow disrupt the process.

Otherwise, stay cool. I would express to the seller in advance my willingness to place a high bid, for example if I haven't found anything better by mid or late February. If there are many bidders, it's better to be the one who names the highest price as late as possible rather than stating a good price early on.

In our case, the group of bidders was private and small. To prevent a bidding war and to introduce some dynamics, we made it clear to the seller that our excellent first and final price was non-negotiable and at the same time credibly limited our interest in the purchase to a specific timeframe, thereby applying pressure to make a decision.

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In our case, the pool of bidders was private and small. To prevent a bidding war and to introduce some dynamics, we made it clear to the seller that our excellent first and final price was non-negotiable and at the same time credibly time-limited our interest in the purchase, thereby creating pressure to reach a decision.

I agree with that. Especially the part about the deadline.

So should we simply make an offer that we consider good and limit it in time? Along the lines of we offer xxx€ and give 2 weeks to accept it?

You have to assess yourself which approach is most sensible with your seller. Is he influenced by deadlines + high price, are there many bidders..? Does it have to be in writing?

I wouldn't call it a "deadline" either, but possibly incorporate a credible story.

How many serious bidders there are, I unfortunately cannot estimate at all :( He wants it in writing so that he can directly assign it to my data, meaning that all our messages are connected. He himself said I should send a "non-binding" offer. I cannot say how the time pressure looks like. When asked, he just said he will wait through February, it should be sold by the middle of the year. I think the seller does not have that much time pressure because of that.