Baugur has a history of buying stakes in struggling U.K. retailers, which subsequently lead to a full takeover bid or the eventual sale of their holding at a good premium.
Last year, Baugur took over Big Food Group, which owns no-frills supermarket chain Iceland Foods.
Iceland Food's performance has improved of late, with the group reporting last month that same-store sales jumped 16.1% in December, with total sales up 10.8%.
Baugur also acquired luxury watches and fine jewelry retailer Mappin & Webb last year. The company also bought fashion retailer Jane Norman together with Kaupthing Bank for GBP117.4 million.
Some investors are hoping that Baugur is working on a takeover offer, which has provided some support to Woolworths' share price in recent weeks.
Others, including Seymour Pierce retail analyst Richard Ratner, are more skeptical about Baugur making a play for Woolworths, and he remains puzzled about Baugur's investment.
"Woolworths' profits are in decline, and it's not exactly rich with assets," Ratner said.
"I just don't think Woolies is very attractive to anyone in my view. They're running it well, it's a case of well- managed, lousy company, and the lousy company is winning," he added.
Ratner has an underperform rating on Woolworths and a 30 pence target price.
At 1255 GMT, Woolworths' shares were virtually unchanged at 36 pence. They are still well short of last year's high of 54.25 pence.