Monk, 38, left Leeds on 25 May after being unable to "reach an agreement" with new owner Andrea Radrizzani.
Since it became apparent that Steve Agnew would not be kept on as first-team boss, both Monk and former Boro defender Nigel Pearson were side to be in the running for the role in the dugout at the Riverside Stadium.
Reading finished third in the Championship but were denied promotion after losing to Huddersfield Town in a penalty shoot-out at Wembley last month.
Radrizzani, who was also interested in Huddersfield's David Wagner prior to Town's promotion, is now weighing up a decision over whether to approach Reading for permission to speak with the ex-Holland global.
UK Conservative Party loses majority, prepares for hung parliament
Though the biggest single victor , they failed to reach the 326-mark they would need to command a parliamentary majority. Being a pro-union party, the joining up of forces may affect May's hopes for achieving a hard Brexit.
Mihajlovic should already be popular with the Leeds United fans, after all he did send Pontus Jansson on loan to Elland Road for the whole of the last season.
Reading manager Jaap Stam is expected to sign a new two-year contract when he returns from holiday, according to the Reading Chronicle.
New managers are about to be in place at Hull City and Middlesbrough football clubs.
Monk was appointed Middlesbrough manager on a three-year deal yesterday.





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