Angelino, 23, spent the second half of last season on loan at Die Roten Bullen and impressed Julian Nagelsmann.
He made 18 appearances for Leipzig, scoring one goal and assisting five for his teammates.
But due to the costs involved, Leipzig did not use their option to buy Angelino for around €30m.
According to Kicker, City are open to letting Angelino return to the Red Bull Arena on loan, but want guarantees.
City insist that a mandatory purchase clause be included in the deal so that Leipzig can’t back out a second time.
The total cost of the transfer would be around €20m and the signs are positive that a solution could be found this week.
Angelino will pen a contract with Leipzig until 2025 if the two clubs agree terms.