Louis van Gaal is exploring the possibility of signing Borussia Dortmund’s Mats Hummels in January for what would be a British record transfer fee for a defender.

The Manchester United manager had earmarked the World Cup winner as a summer target but Ed Woodward, the executive vice-chairman, is hopeful a deal can be done in the winter window. Dortmund may sell reluctantly, believing it would give them the best price for one of their prize assets.

Hummels will have only two years left on his contract next summer. United will try to prise him away early by offering what could well be more than the £32m paid by Manchester City to Porto for Eliaquim Mangala.

Hummels has been hampered by injury and his form since playing in Germany’s 1-0 World Cup final victory over Argentina has been disappointing. Dortmund are fourth-bottom in the Bundesliga with only 10 points.

“We are not looking to enter the market for short-term fixes,” Woodward told investors on Tuesday. “However, we have targets we are looking at for next summer. Should any of them become available in January, which is obviously rare, we will consider acting but it is a low probability.”

In the two previous windows Woodward has signed players in the closing days when the market had seemed to have finished for United. Radamel Falcao was acquired on transfer deadline day at the end of the summer window in a season-long loan from Monaco that is costing United £16m in fee and wages for the striker. Last January Juan Mata was bought in the last week of the window from Chelsea for £37.1m.

Dortmund are expecting a bid for Hummels following Van Gaal’s failed attempt in the summer. Arsène Wenger is another who is an admirer and United may also have to fend off Barcelona – Hummels has previously expressed a liking for the Catalan club.

United can take encouragement from the 26-year-old having made a visit to Old Trafford on Boxing Day 2006 to mark his 18th birthday. He watched Sir Alex Ferguson’s team defeat Wigan 3-1. It is understood Hummels considers United’s status as England’s leading club a particular attraction.

Hummels’s father, Hermann, who advises him on his career, has also observed Van Gaal at close quarters when – as a former lower league player – he worked as the youth team coach at Bayern Munich when the Dutchman was in charge. Hummels Jr was also at Bayern as a teenager so is aware of Van Gaal’s managerial ethos and style.

Van Gaal also continues to monitor Kevin Strootman, the Roma midfielder who made his first Serie A appearance of the season as a substitute in the 3-0 win over Torino. This followed the serious knee injury the 24-year-old suffered last spring.