The 24-year-old started all 38 of Boro's Premier League matches during the 2016-17 campaign, in addition to their season opener in the Championship last weekend against Wolverhampton Wanderers.
However, Gibson has been heavily pursued by several clubs since Boro's relegation from the Premier League, with West Bromwich Albion manager Tony Pulis recently describing him as "a smashing player".
According to Sky Sports News, the Baggies have so far failed with two bids for the centre-back, with the second offer totalling up to £20m, while Southampton have also been linked with the Englishman.
"You want to keep your most important players and the chairman is very strong on that," Monk told reporters. "We don't have to sell anyone. It's a stable club financially and it's a great place to go and work. We're looking to get the squad together, work hard and wait for that window to close."
Asked if he was expecting more bids for Gibson, Monk replied: "Not particularly, no. But I'm not concerned, I'm not focused on that. You can never say never, but in terms of Ben's commitment to the club and the owner's idea of what's needed to be done it aligns with what I'm thinking so it's fine.
"I can't believe [the transfer window] goes into the season. It's ridiculous and should have been shut last week, but we'll stay focused on the season ahead."
Gibson only signed a new five-year contract with Middlesbrough last August.