If the President makes treaties with foreign nations, the Senate must ratify them. Presidents have included Congressmen in delegations that negotiate treaties, but Presidents have never consulted the whole Senate while a treaty was being negotiated.
The President alone is responsible for negotiating treates. For most lesser treaties that task is left to the Secretary of State and the State Department. However, some key treaties such as the ones that were negotiated on nuclear disarmament have been done by the President and his advisors. Often Presidents have involved Congressional delegations in treaty negotiations as a means of gaing support for the treaty that will have to be ratified by the Senate