Does modern philosophy entertain the notion of objective beauty? Are there any sources which discuss such a possibility and do they offer a possible definition of such a concept?
Perhaps you may look to the Hegelian Lectures on Aesthetics. As Hegel's philosophy is regarded Objective Idealism his analysis of the beautiful or of art includes an objective element.
Now when truth in this its external existence [Dasein] is present to consciousness immediately, and with the concept remains immediately in unity with its external appearance, the Idea is not only true but beautiful. Beauty is determined as the sensible shining of the Idea.
Hegel's Aesthetics is regarded by many as one of the greatest aesthetic theories to have been produced since Aristotle.
Hume argues for an objective standard of taste in the aptly named Of a Standard of Taste.
Hume argues that beauty can be objectified and that it is the job of 'true critics' to do so, defined as (having)...
Strong sense, united to delicate sentiment, improved by practice, perfected by comparison, and cleared of all prejudice, can alone entitle critics to this valuable character; and the joint verdict of such, wherever they are to be found, is the true standard of taste and beauty.
Hume's view is that a sufficiently qualified critic through when forming a consensus with other true critics is able to provide an objective standard of taste.
Hume's SoT is a good place to start and its pretty readable.
According to the famous PhilPapers survey, objective aesthetics is slightly more popular than subjective aesthetics, while moral realism is substantially more popular than moral anti-realism. While none of these positions enjoy anything close to a consensus, they're certainly "entertained" in modern philosophy. People might not discuss the aesthetic question as much as the meta-ethical one, though the arguments on each side will bear a lot of similarities. In recent years it's become common to argue that epistemology is normative, so if epistemic norms are "real" other norms may well be; so it's unsurprising realist positions enjoy more popularity than, say, logical positivism, which modern work probably doesn't entertain.