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Villa suffered a big blow earlier this month after their £22m striker Wesley Moraes was ruled out for the rest of the season with a knee injury.
The report claims that Boro boss Jonathan Woodgate is not keen to lose Assombalonga.
Boro broke their transfer record when they signed Assombalonga from Nottingham Forest in the summer of 2017 for a reported fee of £15m.
The 27-year-old has scored six goals and provided two assists in the Championship this season. He is currently out injured but is set to return from an ankle injury within the next two weeks.
Villa are still looking to sign him and are looking to table a formal offer for the striker.
Underwhelming signing for Villa
Signing a striker is a priority for Dean Smith in January, but Villa should look for better options elsewhere.
Assombalonga has proven himself in the Championship, but doubts remain about whether he is good enough to lead the line for Villa in the Premier League.
With Villa fighting for survival, Smith should look to sign strikers with proven Premier League experience, someone like Michy Batshuayi.