The Republic of Ireland international's current contract is set to expire at the end of the season, but Albion are hopeful of fighting off interest and tying him down long-term
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Hull boss Steve Bruce has been linked with another swoop for the former Reading man in January, while Championship side Nottingham Forest are also reported to be lining up an ambitious bid to take Long back to the second tier of English football.
Long is in the final year of his contract, but Downing is eager to ensure the 26-year-old extends his stay at the Hawthorns.
"We are treating it that Shane is very much part of the set-up here," he told the Daily Star.
"The club are actively trying to get him to sign a new deal and we're quite confident of keeping him."
Long has scored just three Premier League goals for Albion this season, but has only started 10 games for the Midlands club.