H&M, which spends an estimated £25 million globally, is not aligned to any international network and is reviewing its media arrangements market by market.
In the UK, the account is held by Universal McCann, which won the £2.5 million business in 2000 from CIA Conzept.
H&M now operates 945 wholly owned stores in 18, mainly European, countries and has 40,000 employees. It has announced ambitious expansion plans with a further 140 stores due to open, including five in Canada and its first in Slovenia.
H&M's biggest markets are Germany, Sweden, the UK and Norway. Its advertising is concentrated in press and posters, and in the past has featured celebrities including Jade Jagger, Tim Roth and Chloe Sevigny.
One outdoor ad campaign last year for H&M featuring the German supermodel Heidi Klum proved so popular that fans were ripping posters off walls and damaging hoardings to get at the pictures underneath.
The recent cold weather has improved H&M's results with January sales up 14 per cent on the same period last year.