FRANKFURT - Germany's Covestro should engage in formal takeover talks with Abu Dhabi National Oil Co (ADNOC) in the interest of its shareholders, two top-15 investors of the plastics and chemicals maker told Reuters.

ADNOC, which is trying to diversify and develop its downstream and renewable energy operations, made a non-binding offer for Covestro of 55 euros per share in June, which was rejected, according to press reports.

Earlier this month, ADNOC verbally signalled to Covestro, which has not officially commented on the takeover approach, that it could raise its informal offer to 60 euros per share conditional on the German company entering formal talks, Reuters reported.

Arne Rautenberg, fund manager at Union Investment, said management should take the next step to enter formal discussions within days to avoid further speculation and market uncertainty.

The higher offer would value Covestro, which produces foam chemicals used in mattresses, car seats and insulation for buildings, at about 11.6 billion euros ($12.58 billion).

The second shareholder, who asked to remain anonymous, warned that with takeover rumours circulating since June, further uncertainty could push Covestro's shares, currently trading at 47 euros, lower.

Covestro declined to comment.

Covestro is among companies in Germany's chemicals sector facing a substantial drop in demand as customers de-stock in a high inflation environment.

Beyond price, the two parties will need to agree on location and jobs, Rautenberg and the other shareholder said, with the latter adding that there seemed to be interest in keeping the firms separate and Covestro remaining independent.

While ADNOC would be achieving a "good deal" at 60 euros per share, it is likely that Covestro wants a higher price still, Rautenberg said, pointing to a share price peak of around 95 euros in January 2018 and the company's growth through acquisitions since its 2015 listing.

Covestro's shares trading below the reported offer price suggests scepticism that a deal will happen, Rautenberg said, although the other shareholder pointed to broader pressure on stocks emanating from Chinese economic weakness.

Rautenberg declined to comment on the price at which he would recommend Covestro accept an offer.

Covestro this week appointed Christian Baier as chief financial officer, with Rautenberg noting his past dealmaking experience at private equity firm Permira. ($1 = 0.9217 euros)

(Reporting by Emma-Victoria Farr, editing by Elisa Martinuzzi, Kirsten Donovan)