It is grammatically correct to use either “I look forward to” (simple present tense) or “I'm looking forward to” (present continuous tense). The major difference has to do with how formal or informal you want to sound. More Informal Use: “I'm looking forward to …”

Can we just say looking forward?

If you mean both in the sense of anticipating something, both are equally valid. However 'I look forward' is more formal; it's the kind of thing you would write in an official letter. A typical example is the closing statement of a cover letter for a job application: I look forward to hearing from you soon.

What can I say instead of looking forward?