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.