Nope. Rei is his mother. That's why Gendo has an attachment to her, because Rei is the clone of his wife. If it was a clone of shinji, that'd just be gross... in a hot way.
Also, when Shinji comments on the way Rei scrubbed the classroom floor, he says it looked, "Motherly". Rei blushed and said something to the extent of "You... You don't say?"