I don't think Chelsea would even have a big chance to sign Osimhen now. Because they won't even be a part of the Champions League next season most probably.
There is no way they are catching up with top four first of all. Apart from that they have to win the Champions League title this season to be able to qualify for the tournament again. But it is also a far possibility to be realistic. I don't think Osimhen would like to join a team that aren't joining the biggest tournament in Europe. Manchester United are another interested team in him these days and they are likely to join the Champions League also. I guess Osimhen would be closer to them if he decides to leave.