Copy and pasted from a similar post:

There wasn't ever an offer to include adequate representation from the British government before the American Revolution. There was an offer during the war however it isn't as straightforward as it may seem.

The event you are referring to is the Carlisle Commission which met with the Continental Congress in 1778 as it attempted to get the United States Congress to end the war with a truce under an agreement of self-government. The agreement however was very backhanded, with some of the members being accused of trying to bribe at least some of the delegates of congress to agreeing to the terms. (Specifically, Robert Morris and Joseph Reed were two that were known at the time. Chris Coelho, Timothy Matlack, Scribe of the Declaration of Independence, McFarland Publishing, 2013. PP 111)

Included in the deal was some semblance of self-government and some representation within Parliament, however most delegates did not find the terms appealing. The Continental Congress wanted independent rule set aside from Great Britain, which the commission members were not empowered to grant. Also, aligned with this was fears that the offer would actually carried out with on the British side. Most of the American representatives guessed (correctly) that the British motivation was to prevent an American-Franco alliance, which they were on the verge of creating.

The Continental Congress ultimately responded with saying, "The Continental Congress declares that “the United States cannot hold with propriety any conference or treaty with any commissioners on the part of Great Britain unless they as a preliminary thereto, either withdraw their fleets and armies or else in positive and express terms acknowledge of the said states.". Great Britain obviously refused this deal since the representatives had no such authority to end hostilities. Regardless, the commission spent a comparatively short amount of time with them in Pennsylvania before being dismissed.