Bellingham is already a fascinating central midfielder and he is playing attacking focused which would be very useful for Chelsea. He has already got 5 goals and 2 assists in 15 matches. On the other hand, signing Bellingham would be a much more difficult task for Chelsea because they won't be the only team after him surely. We might see Real Madrid joining the race and then Chelsea wouldn't stand much chance to sign him. I guess he wouldn't prefer Chelsea to Real Madrid. 
Before Chelsea plans to sign Bellingham, Real Madrid already tried to sign him first. So, Real Madrid isn't joining the race but Chelsea is joining race.I agree that Bellingham should prefer to move to Real Madrid. Chelsea has no power to sign Bellingham, Real Madrid is the favorite team. In my opinion, Chelsea seems impossible to sign Bellingham, they will have no chance. I suggest Chelsea to look for another player.
If he will have a non sense price and i think that real madrid will think again before try to signing him with a non sense price like that. We will see where he will be going on.