That's right, we're unlikely to have any VAT costs ourselves, but if Liverpool shelled out a headline figure of £7m, its likely that the gross inclusive VAT amount would actually be £8.4m.
However, as Liverpool are making fully taxable supplies e.g. sale of tickets, merchandise, catering, booze, players etc, they should be able to pay City the £8.4m but recover £1.4m from HMRC through their VAT return. City would have also had to pay over the £1.4 m VAT to HMRC that they collected.
Assuming Latics recieve 20% of £7m = £1.4m, we would invoice City for £1.4m + £280k VAT = £1.68m, we would pay over £280k to HMRC but City would be able to recover £280k themselves.