In general, I'm not a fan of buying players instead of giving chances to the homegrown, as it's much better for the future of a club to trust in its youngsters. Nonetheless, signing Özil would definitely boost our quality and therefore our chances of winning the CL. I'm sure he has 2-3 great seasons in him. I know the club is much more important than one player, but to be honest i would be tremendously pissed of if Messi and CR would end up with the same amount of Ballon d'ors and CL-trophy and if people would argue that they were on the same level after their retirement. Therefore the next 3 seasons will be crucial to give Leo at least two more CL titles and signing Özil would definitely increase our chances winning it tremendously for the next few seasons. Moreover, 20 Mio for a high quality player (and Özil definitely is one of them) is a steal in todays market.
Therefore, I think it wouldn't be that bad if we sign him in january. Only thing I hope is that we sell at least two midfielders if we really sign him. I would therefore sell Gomes and Rakitic. With Busi, Iniesta, Özil, Roberto and Paulinho we would have a great midfield. I think it would also be possible to give some minutes to Aleña then. If we may have some serious problems with injuries, we still have Denis and Masche who could also play in midfield.