Washington is ready to extend the Strategic Offensive Arms Treaty (START-3), subject to the conditions that the OP sets.
This was reported by the Wall Street Journal, citing its source among representatives of the presidential administration Donald Trump.
For example, Trump may agree to extend the Treaty if the parties make progress in including new stringent verification measures, if all nuclear warheads are taken into account, as well as if China joins it.
Moreover, it is far from a fact that this is all that the American president wants. It is possible that he will come up with some other conditions.