Dresdner Kleinwort Wasserstein had placed the shares on Mr McClay’s behalf at 810 pence each, the sources said.
Both Galen and Dresdner declined to comment.
Analyst at Dublin’s Dolmen Securities Stuart Draper, said the extra supply of Galen stock on the market could push the shares down to about 800p.
“The stock has risen around 18% since the start of January, so it has come a long way and the fact that it is being placed at a discount to yesterday’s price would indicate this is not a ludicrously low level for it,” he said.
“We were of the view yesterday that at 848p it seemed reasonably well valued and the fact Mr McClay has done this might suggest he is also of that view.”
But John Wilson, an investment director of Standard Life Investments, which owns more than 3% of the stock, said the sale was no surprise.
“Obviously the founder is selling the last of his stock and he has been selling fairly steadily over the last few years and this is just the culmination of that,” he said.
“You can never be sure of the timing of these things but there was no real surprise.
“It’s just a continuation of what he had been doing because he’s no longer involved in the day-to-day running of the business. The story is still intact,” he added.
Mr McClay, who founded the Co Armagh-based drugmaker in 1968 and retired in 2001 aged 69, sold 700,000 shares at 710.5 pence each in July, leaving him with a holding at that time of 8.9%.