высасывать из пальца {v. phr.}
{literally}
To suck something out of one's finger.
~ to make (d) up out of whole cloth.
To fabricate smth, dream the whole thing up.
To allege something which has no foundation in actual fact, absolutely groundless; to fabricate.
Comp.:
to make something up
to spin something out of thin air
See also:
притягивать за уши