The Germany international is one of Europe’s most sought after attackers, with a £20m release clause in his BVB contract due to kick in at the end of the season.
And with Dortmund struggling in the Bundesliga – they currently sit in the relegation zone – there are suggestions that the versatile forward may leave before the January transfer window closes.
A host of big sides are chasing Reus, but Mourinho is desperate to make sure that Chelsea come out on top.
The Portuguese coach is understood to have told Russian billionaire owner Abramovich that the 25-year-old is the player he wants above all others this month, as he plots to ensure that the Blues’ positive start to the season ends with the Premier League title.
Chelsea are known for their lavish spending, but a summer in which they turned a profit is rumoured to have left funds in place for at least one big winter addition.
Other reports suggest that Real Madrid have all but agreed a move for Reus at the end of the season.