The Danish international has been on the radar of the Premier League outfit for some time, following multiple impressive performances with the Amsterdam club both domestically and in Europe.
The 20-year-old has previously claimed to be happy in Holland and keen to remain at the Amsterdam ArenA for the foreseeable future.
However, Ajax director, and former Arsenal player, Marc Overmars told reporters that the youngster has changed his mind, and may attempt to leave the club:
“We would like Christian to sign a new contract with us, but it’s not something he wants.” He told Sporten in Denmark.
“We will see what happens after this year. We speak with him and his agent and we will see what happens after December.”
With his current deal set to expire in 2014, the midfielder could be available at a reduced fee during the coming transfer windows.
United have been heavily linked with the starlet in recent months, with Sir Alex Ferguson keen to add his creative talents to the Old Trafford armoury.
Liverpool are another interested party, with reports claiming that Brendan Rodgers sees the playmaker as the ideal long-term replacement for club captain Steven Gerrard.