June 11 (Reuters) - Shares in Hugo Boss rose about 7% on Thursday after Britain's Frasers Group launched a $2.3 billion takeover offer for the German fashion brand.

Frasers, already the largest shareholder of Hugo Boss with a stake of just over 26%, is offering €38 per share in cash for the remaining shares, a 4.3% premium to Wednesday's close.

Hugo Boss said late on Wednesday the approach was not coordinated with the company and that its board would review the offer, which values the stake not yet owned by Frasers at about €1.98 billion ($2.3 billion).

The deal would bring Hugo Boss into the retail empire controlled by British billionaire Mike Ashley, whose Frasers Group owns Sports Direct and House of Fraser and holds stakes in Asos, Debenhams and Currys.

J.P. Morgan said the bid likely sets a near-term floor for the shares but flagged limited scope for further upside, adding it did not expect a rival bidder to emerge.

Hugo Boss, whose shares are about half their level of three years ago, has been struggling with weaker sales and is pursuing a turnaround strategy focused on store revamps, a streamlined product range and expanding women's wear.

By 0713 GMT, Hugo Boss shares were up 6.2% at €38.7, above Frasers' offer price, taking their year-to-date gains to 7.2%. Frasers shares fell 2.5%.

($1 = 0.8664 euros)