The Nerazzurri are expected to strengthen their squad significantly in the January transfer window and next summer after the Suning Holdings Group purchased a majority stake in the club in June.
The Italian giants have been credited with an ambitious move for Costa, with speculation suggesting they will test Chelsea's resolve with a bid in the region of £50million for the striker.
However, sporting director Piero Ausilio has moved to reject the rumours and says Inter are happy with their present options in attack.
When asked about Costa, he told Premium Sport: "To talk about this is absurd, we already have a very strong centre-forward [Mauro Icardi].
"We will try to evaluate the positions we feel need strengthening."