Australia's Perpetual says EQT's $1.78 billion bid not in best interests of shareholders

July 29 (Reuters) - Australia's Perpetual said on Wednesday that EQT AB's latest A$2.55 billion ($1.78 billion) takeover proposal was not in the best interests of shareholders, but that it would grant the Swedish buyout firm limited due diligence access as it considers a possible improved offer.

Here are some more details:

• On Monday, EQT offered to pay A$22.50 per Perpetual share in the latest bid, higher than its two earlier offers and a 19% premium to the Perpetual stock's Friday close.

• EQT has progressively sweetened its offer as it pursues the Australian wealth manager and trust business, with the latest proposal representing a roughly 4% increase from its initial approach.

• EQT did not immediately respond to a Reuters request for comment outside regular business hours.

($1 = 1.4339 Australian dollars)

(Reporting by Jasmeen Ara Shaikh in Bengaluru; Editing by Subhranshu Sahu)