Howson had initially been linked with a return to former club Leeds United, where he spent the first six years of his professional career.
However, Garry Monk's switch to Middlesbrough has seen plans change and according to The Mirror, Monk wants to take the midfielder to the Riverside Stadium.
It has been claimed that Norwich are looking for £5m for the 29-year-old, and it appears that Boro - who have just been relegated from the Premier League - are willing to meet their valuation.
Howson has spent the past seven seasons as a regular in the top two divisions in English football, and his acquisition would provide Boro with a boost ahead of their return to the Championship.
The former England Under-21 international has scored 24 goals in 174 appearances for Norwich in all competitions.