Speaking at a media conference at Rockliffe, Monk said he was excited by the "ambition" at Boro and relishes the "challenge" of getting the club back into the Premier League.
Monk also spoke to Sunderland, but made a decision to take on the challenge at the Riverside to try and achieve an immediate return to the Premier League after their relegation last season.
However, new Boro manager Garry Monk is reluctant to see his captain sold.
During the January transfer window, Garry Monk had a plan to land the 26-year-old midfielder and to strengthen this part of his team.
Monk has joined Boro on a three-year contract just over two weeks after leaving Leeds United following his one-season stay at Elland Road, where he just missed out on a play-off place.More news: Police arrest 2 more suspects over bridge attack
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But having received assurances from the player's uncle, club owner Steve Gibson that he does not have to sell his prize asset, Monk hopes to convince the centre-half to commit himself to next season's promotion campaign. It was a situation where I went into Leeds, a fantastic club, and got to work straight away.
"I don't want to go into details out of respect for Leeds but it was a new ownership and a new structure".
Monk has yet to finalise his backroom staff or decide the future of former head coach Steve Agnew and won't meet his players until they report back for pre-season training later this month.
However, his agent Henk Timmer has told Voetbal International, that Stam will remain loyal to Reading FC who gave him his big chance in England unless a big club from the Premier League come knocking.
"It's important that we keep our best players, and the club are in agreement with that".