An Championship club made a bid for 21-year-old Hutchinson while a League One club failed in an approach for English midfielder Law.
'Well boss Stuart McCall told the club's official website: "Whilst we understand every player at this club has a value, we also need to ensure we protect our interests by getting the right price for our talent.
"Rejecting both offers, which were significant in Motherwell terms, is also a sign of intent from the club's board that they are not prepared to accept any bid that comes our way.
"Unless a vastly-improved offer comes in then it is business as usual."
Newcastle-born Hutchinson has become Motherwell's first-choice centre-back under McCall after making his debut in 2009. He was previously the suvject of an offer from Watford.
"Shaun has been terrific for us since I arrived at the club and has been a virtual ever-present in that time," McCall said.
"He has all the raw materials you would want from a centre-back - he's young, big and powerful and the experience of playing in the Europa League and Champions League is standing him in good stead.
"He is already a top player, I would say he's one of the hottest young talents in the SPL, and we are certain he'll mature into an even better defender as his experience grows. That's why any offer for him needs to be realistic."
Creative midfielder Law, 24, signed a two-year contract when he joined from League Two club Rotherham last summer, and has proved a big hit with the Motherwell support.
"Nicky has been the cornerstone of a lot of success going forward over the last 12 months and is vital to us," McCall said.
"His contribution from midfield was key in qualifying for Europe last term and any offer for him would have to reflect his contribution to our side."
