The US have formally announced that they intend to open trade negotiations with the UK (alongside the EU and Japan). Whatever the outcome of the Brexit negotiations, assuming the UK leaves the EU on 29 March 2019 it will be free to start negotiating its own free trade agreements.
If there is an 'orderly Brexit' and the transition arrangements take effect then the UK will be free to negotiate new trade agreements with the rest of the world, although it won't be able to give effect to those agreements until the end of that transition period (currently scheduled for 30 December 2020).
In the event of a 'hard Brexit' there will be nothing to formally stop the UK negotiating and concluding new agreements from day 1. However, even in the event of a hard Brexit there are two main stumbling blocks to concluding a new US agreement. First, the UK's biggest economic partner will remain the EU, by far. A hard Brexit does not mean that a new UK-EU trade agreement can't be negotiated, albeit that the ill-will and rancor (on both sides) may make that more difficult than it needs to be. Many other countries will remain keen to see what the shape of that UK-EU trade deal looks like before starting – or at least before concluding – their own negotiations: What access will the UK have to the EU markets? What tariffs or quotas will be in place (if any)? What commitments on regulatory harmonization will be made? The list goes on …. The second main stumbling block is time. Trade agreements are complicated. The EU and Canada agreement took 7 years to negotiate and even if you discount the 2 years wasted on political squabbles (and who knows what squabbles may emerge with the US) these trade deals cover a whole range of issues that simply take time to negotiate.
So, the latest announcement from the US remains a piece of theatre for now with a long way to go - and little compensation for any failure in the Brexit negotiations - but perhaps some compensation for the Prime Minister in a difficult week ...