Looking forward/forwards to your reply [duplicate]

Forward and forwards are similar, and people often confuse them. According to this blog, however, you shouldn't worry too much about which is correct when you are using them as adverbs:

Forwards is a variant spelling of the adverb (not the adjective) forward. (e.g., We moved forward/forwards in the forward [not forwards] compartment.) Towards is a variant spelling of toward. Use whichever sounds better to you, but be consistent.

However, in the case of look forward to, this is an phrasal verb. It is never written with forwards:

So you should say I am looking forward to.... When you are using forward as an adverb, however, you can pick which one you prefer. Both of the following are correct:

I moved forward in line

I moved forwards in line

The question of "forward vs. forwards" in terms of adverbs is explained here in an older question.

The Corpus of Contemporary American English doesn't have a single match for the phrase "looking forwards" and it sounds like a mistake to me. So you should say

Looking forward to your reply.