Federal prosecutors sent indicted state politician Sheldon Silver a letter laying out his likely sentence if he pleaded guilty on all corruption charges — but he never responded, they revealed in court Friday.

“More than a month ago the government sent the defendant a . . . letter and no response was given,” assistant US Attorney Carrie Cohen said during the last pretrial hearing before Silver’s trial next week, adding, “Defense counsel has never asked for a plea ­offer.”

Manhattan federal Judge Valerie Caproni rejected five prospective jurors after prosecutors and defense attorneys objected to answers they gave on questionnaires they filled out earlier in the week.

“It would be interesting to have a jury consultant sitting on the jury, wouldn’t it?” joked Caproni, before dismissing that juror because of planned business travel during the trial.

“That’s one way to look at it, your honor,” Cohen replied.

Jury selection for Silver’s trial begins Monday.