His move to reassure fans comes amid reports Championship rivals Nottingham Forest have made a fresh bid to sign Grant Leadbitter from the Riverside outfit.
But Mowbray says the club are trying to put a team together to compete in the division.
The Middlesbrough boss told the Evening Gazette: "I don't think our supporters should be concerned about any of our best players leaving.
"The chairman is very supportive about the fact that we are trying to build a team to get out of this league.
"Why would you sell your best players to your potential rivals? I don't think that's something we should be concerning ourselves about.
"We're trying to build a team not dismantle one or chase money.
"We're trying to put together a team that can be competitive at the top end of the table."