Barslaser is being targeted by Middlesbrough as they want to deepen their midfield department and provide competition for Jonny Howson and Hayden Hackney.
Middlesbrough presented an offer earlier in the window for the 26-year old but it was rejected by Rotherham.
The midfielder’s contract with Rotherham is up in the summer and they risk losing him on a free transfer if he is not sold this window.
Now Middlesbrough are expected to go in and submit another bid for Barlaser to Rotherham as Boro continue their pursuit despite the previous setback.
It remains to be seen if Middlesbrough’s new offer is able to persuade Rotherham to depart with the Newcastle United academy product.
Middlesbrough are also interested in Barlaser’s team-mate Chiedozie Ogbene, who is similarly out of contract in the summer.
Barlaser played a key role in helping Rotherham earn promotion to the Championship last season and has played in every one of the Millers’ league games this term.