The 30-year-old joined the Citizens on a free transfer from Arminia Bielefeld last summer and has since provided cover for first-choice shot-stopper Ederson.
Ortega made only 14 appearances for Pep Guardiola's treble-winning side last season, including just three Premier League starts and two outings in the Champions League.
However, the German shot-stopper was an integral part of City's success en route to FA Cup glory, starting all six matches and keeping five clean sheets.
Ortega was handed a start between the sticks in the Community Shied defeat on penalties to Arsenal earlier this month, but he was replaced by Ederson for City's opening Premier League game of the new season against Burnley last Friday, in which the reigning champions won 3-0 at Turf Moor.
Ortega has two years remaining on his contract at the Etihad Stadium and Man City are believed to be keen to offer the goalkeeper a new and improved deal.
However, according to Sky Sports Deutschland journalist Florian Plettenberg, Bayern Munich have identified the German as their top goalkeeper target.
Plettenberg adds that the perennial Bundesliga winners have held talks with the player's representatives in the last few days over a summer switch to the Allianz Arena.
Ortega will now weigh up a potential move to Bayern, but Guardiola is said to be confident that the German will stay at Man City and extend his contract.
Bayern have turned their attention to signing Ortega following the permanent departure of Yann Sommer to Inter Milan and the injury concerns over 37-year-old Manuel Neuer, who is still recovering from a broken leg sustained last December.
Bayern currently have Sven Ulreich filling in between the sticks, but head coach Thomas Tuchel is hoping to sign a new number one before next month's transfer deadline.
The German giants had been interested in signing Kepa Arrizabalaga from Chelsea, but the Spaniard has instead joined Real Madrid on loan.
The likes of Sevilla's Yassine Bounou and Ajax's Geronimo Rulli are both believed to be on Bayern's shortlist, but Ortega is the man Tuchel wants as his new number one.
Bayern will look to step up their pursuit of a new goalkeeper now that they have completed the club-record signing of striker Harry Kane from Tottenham Hotspur.
Ortega has travelled to Greece as part of Man City's 22-man squad for Wednesday's UEFA Super Cup clash with Sevilla.