Nothing is stopping you, although it’s unusual for the consultant to bring it up. There’s a good chance the company hiring you will ask you to sign a non-disclosure agreement (NDA) the first day. In that case, make sure the agreement you sign is a bilateral NDA.
A bilateral NDA is a contract wherein both parties agree to keep information exchanged between them a secret. Many attorneys advise on a mutual NDA in all cases in order to draft the provisions to be fair and equal for both sides in the event that the information receiving party later becomes a disclosing party.
If you’re looking for lawyers with experience drafting NDAs for tech businesses and consultants, then feel free to check out.