Question

Did Decimus Brutus actually offer Caesar the title of King in the Ides of March?

I finished reading "Julius Caesar" by Shakespeare and in my mind came up the question, did Decimus Brutus really say to Caesar that the Senate was going to crown him King to lure him to his death, or is that just Shakespeare, making his play more dramatic?

Of course, I know that they were not going to crown him King, but I would be interested to know if Caesar went to the Senate that day expecting to be crowned as King of Rome.