I understand that perception of the buying / selling process - it’s a popular one but, with due respect, I hold that it doesn’t work like that.
I think you’ll find that football clubs carry out an assessment of needs exercise and decide a maximum price that they’ll pay (the buying club) and a minimum price that they’ll sell for (the selling club obviously).
If those figures meet then the player gets bought / sold and if they don’t then the selling clubs valuation is above the market value, as is often the case, and a sale doesn’t happen.
The reason for the poker playing between the parties is that there can be quite a wide crossover so that both clubs will want to maximise their position (buying club wanting to pay less than their maximum and selling club wanting to receive more than their minimum) - though it can still ultimately transpire that there’s a gap between the two.
The added complexity is that the clubs valuations can fluctuate during the process due to matters like the replacement player being more or less expensive than anticipated or the purchasing clubs alternative being more / less expensive than anticipated or simply not available etc.
The days of chairmen spitting in their palms and shaking hands on an artificial mid-point value (we want to pay 30 you want to receive 50 so let’s call it 40) are long gone - if they ever existed in the first place except in movies.