Sterling jumped one percent against the euro to 90.15 pence and has risen 1.15 percent against the US dollar to $1.3537.
MUG strategist Lee Hardman said: "The market is anticipating that a deal will be agreed in the next day or two.
He added the pound could strengthen to $1.36/$1.37 but traders are first keen to see details of any agreement.
Mr Hardman continued: "The best case scenario for the pound would be if we also see details released form the EU and UK side of things alongside the deal to try and reduce the initial disruption when we shift to a new trading arrangement."
A senior EU diplomat had earlier told Reuters a post-Brexit trade deal between the UK and EU could be agreed as early as Wednesday evening.
The insider said EU member states would still have to approve a provisional application of the deal with effect from January 1 as time has run out for the European Parliament to ratify it.
Three diplomatic sources told Reuters the bloc's member states have started to prepare their procedure to implement any deal from the statrt of next year.
One EU diplomat said: "It seems the deal is pretty much there. It's a matter of announcing it today or tomorrow."
A Downing Street source said it is "possible but far from certain" that a post-Brexit trade deal could be agreed between the UK and EU on Wednesday.
The increased possibility of an imminent trade deal has also seen gilt yields rose with 10-year yields up more than eight basis points to 0.27 percent.
German 10-year yields jumped 5.5 basis points.
Eurasia Group Managing Director Mujtaba Rahman told clients: "On process, the Commission is very keen to strike a deal by tomorrow evening at the latest, as it fears it will otherwise be difficult to even provisionally apply a deal for January 1."
Negotiators from both sides continue to be locked in discussions over a post-Brexit trade deal as the end of the transition period on December 31 deaws closer.
Boris Johnson and European Commission president Ursula von der Leyen also remain in close contact to try to resolve remaining difficulties.
The Prime minister has repeatedly said it is likely talks will end with a no-deal outcome, with the UK then relying on World Trade Organisation (WTO) terms.
This would mean the imposition of hefty tariffs and quotas on goods with the EU.
Earlier on Wednesday, Cabinet minister Robert Jenrick said he is "reasonably optimistic" that a deal can be struck before the end of the transition period.
But he warned "serious areas of disagreement" remain on fishing and the level playing field measures aimed at preventing unfair competition on standards and state subsidies.
Mr Jenrick told Sky News: "We are working through those issues, our negotiators will keep going - the Prime Minister has been very clear that he is going to negotiate until the very end, which is December 31, because that is the right thing, it is what the British public would expect.
"But at the moment there isn't sufficient progress, it isn't a deal that the Prime Minister feels he can sign us up to because it doesn't yet respect us, in full, as a sovereign, independent nation."
French Europe minister Clement Beaune had warned the EU should not put itself under pressure to agree a trade deal with the UK at the eleventh hour.
He claimed a no-deal outcome would be "catastrophic" for Britain and suggested the EU should hold out.
Mr Beaune said: "We should not put ourselves, Europeans, under time pressure to finish by this hour or that day.
"Otherwise we would put ourselves in a situation to make bad concessions."
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