Dionys. Hal. A. R. I, c. 72: (Fowler 2000,68; Damastes fr. 3)
“After summarizing the sacrifices in Argos and how everything was done with each, he says that Aineas came from the Molossoi to Italy with Odysseus and became the founder of the city. And he named it.”
῾Ο τὰς ἱερείας τὰς ἐν ῎Αργει καὶ τὰ καθ’ ἑκάστην πραχθέντα συναγαγὼν Αἰνείαν φησὶν ἐκ Μολοττῶν εἰς ᾿Ιταλίαν ἐλθόντα μετ’ ᾿Οδυσσέως, οἰκιστὴν γενέσθαι τῆς πόλεως· ὀνομάσαι
As Fowler (Early Greek Mythography 2. 2013, 564-5) notes, the Greek could mean either that Aeneas came to Italy with Odysseus or came to Italy and founded the city with Odysseus. Either way, the story is certainly not one at home in our Odyssey.
Note though that the close collocation of Odysseus and Aeneas appears in Hesiod’s Theogony too (1008-1013):
“And well-crowned Kythereia gave birth to Aeneias
after having lovely sex with the hero Anchises
on the hills of windy Ida with its many valleys.
And Kirke the daughter of Helios the son of Hyperion
after sex with enduring-minded Odysseus
gave birth to Agrios and blameless and strong Latinus.”
Αἰνείαν δ’ ἄρ’ ἔτικτεν ἐυστέφανος Κυθέρεια,
᾿Αγχίσῃ ἥρωι μιγεῖσ’ ἐρατῇ φιλότητι
῎Ιδης ἐν κορυφῇσι πολυπτύχου ἠνεμοέσσης.
Κίρκη δ’ ᾿Ηελίου θυγάτηρ ῾Υπεριονίδαο
γείνατ’ ᾿Οδυσσῆος ταλασίφρονος ἐν φιλότητι
῎Αγριον ἠδὲ Λατῖνον ἀμύμονά τε κρατερόν τε·
It may be important that a possible reference is here too to Italy (in the name Latinus). In other texts, there is still an indirect association between Aeneas, Odysseus and the founding of Rome:
Geoponica, 220.127.116.11 (10th Century CE)
“For they say that Latinus was the brother of Telegonos and the son of Circe. and the father-in-law of Aeneas, that he founded the Akropolis before Aeneas arrived, and discovered laurel there.”
τὸ παλάτιον ὠνομάσθη, ἀπὸ τῆς ἐπικλήσεως δάφνης τῆς ἐν ῾Ρώμῃ. φασὶ γὰρ Λατῖνον τὸν Τηλεγόνου μὲν ἀδελφόν, Κίρκης δὲ παῖδα, πενθερὸν δὲ Αἰνείου, κτίζοντα τὴν ἀκρόπολιν πρὸ τῆς Αἰνείου παρουσίας, εὑρηκέναι ἐκεῖ δάφνην.
Aelian claims that the Greeks let Aeneas go: Varia Historia, 3.22
“After they captured Troy, the Greeks pitied the fate of the captured people and they announced this altogether Greek thing: that each of the free men could select and take one of his possessions. Aeneas selected and was carrying his ancestral gods, after dismissing everything else. Impressed by the righteousness of this man, the Greeks conceded that he may take a second possession away. Then, Aeneas placed his father—who was extremely old—on his shoulders and walked off. Because they were so amazed, they granted him all of his own possessions, attesting to the fact that men who are enemies by nature become mild when faced with righteous men who revere the gods and their parents.”
῞Οτε ἑάλω τὸ ῎Ιλιον, οἰκτείραντες οἱ ᾿Αχαιοὶ τὰς τῶν ἁλισκομένων τύχας καὶ πάνυ ῾Ελληνικῶς τοῦτο ἐκήρυξαν, ἕκαστον τῶν ἐλευθέρων ἓν ὅ τι καὶ βούλεται τῶν οἰκείων ἀποφέρειν ἀράμενον. ὁ οὖν Αἰνείας τοὺς πατρῴους θεοὺς βαστάσας ἔφερεν, ὑπεριδὼν τῶν ἄλλων. ἡσθέντες οὖν ἐπὶ τῇ τοῦ ἀνδρὸς εὐσεβείᾳ οἱ ῞Ελληνες καὶ δεύτερον αὐτῷ κτῆμα συνεχώρησαν λαβεῖν• ὃ δὲ τὸν πατέρα πάνυ σφόδρα γεγηρακότα ἀναθέμενος τοῖς ὤμοις ἔφερεν. ὑπερεκλαγέντες οὖν καὶ ἐπὶ τούτῳ οὐχ ἥκιστα, πάντων αὐτῷ τῶν οἰκείων κτημάτων ἀπέστησαν, ὁμολογοῦντες ὅτι πρὸς τοὺς εὐσεβεῖς τῶν ἀνθρώπων καὶ τοὺς θεοὺς καὶ τοὺς γειναμένους δι’ αἰδοῦς ἄγοντας καὶ οἱ φύσει πολέμιοι ἥμεροι γίνονται.
Pausanias also has a strange account that Aeneas traveled through Greece proper and that Anchises died there
“Of the roads leading to Orkhomenos there remains the one that goes by Mt. Anchisia and a monument to Anchises near the base of the mountain. When Aeneas was traveling to Sicily, he stopped his ships near Laconia and founded the cities Aphrodisias and Etis. His father came to his area for some reason and died. Aeneas buried him there. For this reason they named the mountain for Anchises. The Aiolians who live Troy near Troy now offer some support for this since they have no monument to Anchises in their land.
λείπεται δὲ ἔτι τῶν ὁδῶν ἡ ἐς ᾿Ορχομενόν, καθ’ ἥντινα ᾿Αγχισία τε ὄρος καὶ ᾿Αγχίσου μνῆμά ἐστιν ὑπὸ τοῦ ὄρους τοῖς ποσίν. ὡς γὰρ δὴ ἐκομίζετο ἐς Σικελίαν ὁ Αἰνείας, ἔσχε ταῖς ναυσὶν ἐς τὴν Λακωνικήν, καὶ πόλεών τε ᾿Αφροδισιάδος καὶ ῎Ητιδος ἐγένετο οἰκιστὴς καὶ τὸν πατέρα ᾿Αγχίσην κατὰ πρόφασιν δή τινα παραγενόμενον ἐς τοῦτο τὸ χωρίον καὶ αὐτόθι τοῦ βίου τῇ τελευτῇ χρησάμενον ἔθαψεν ἐνταῦθα· καὶ τὸ ὄρος τοῦτο ἀπὸ τοῦ ᾿Αγχίσου καλοῦσιν ᾿Αγχισίαν.τούτου δὲ συντελοῦσιν ἐς πίστιν Αἰολέων οἱ ῎Ιλιον ἐφ’ ἡμῶν ἔχοντες, οὐδαμοῦ τῆς σφετέρας ἀποφαίνοντες μνῆμα ᾿Αγχίσου.