On Thursday the euro hit a low of 1.0364 against the dollar, the lowest level since August 2003 when it traded as low as 1.0357.
Dollar strength is the key driver as investors believe the Federal Reserve will adopt a higher rate rise path in 2017 as the U.S. economy gathers momentum.
Analysts at ING wrote Friday that with European inflation struggling to edge higher and yesterday's dip in to the 1.03 handle, euro/dollar parity is now firmly in view.
"With the U.S. economy close to reaching escape velocity (and sustainable 2 percent inflation), it will only reinforce the downside risks to EUR/USD."
"Expect some consolidation around the 1.0450-1.0500 area, but this week's fresh EUR/USD low means that the move down to parity is now only a matter of time," the note reads.
The research team at Unicredit said in their note Friday that while the current sell-off in the euro is probably overdone, thin trading volumes at Christmas may well see it move lower.
"The momentum is very strong and the break of key thresholds on daily charts, and in particular the 1.05 baseline for EUR-USD, may trigger more weakness in the coming days."
"This, together with the usual very thin liquidity conditions at the end of the year, may reinforce the decline too," said the note.
If euro/dollar falls to parity before the end of 2016, history shows it could spell trouble for investors hoping for a "Santa Claus rally".
Data from Kensho has analyzed what happens to U.S. stock markets should the euro lose 4 cents within a two week time frame. This has occurred 42 times in the last decade.
It found the Dow posted an average decline of 1.6 percent and was positive on only 40 percent of those occasions.