Mourinho needs a striker because of a back injury which could sideline Gonzalo Higuain for up to two months.
Manchester City misfit Adebayor tops the list Mourinho gave to club president Florentino Perez and general manager Jorge Valdano on Thursday. The manager is confident he can seal a loan deal for the 26-year-old.
Loan bid: Adebayor
Swap deal: Hernandez
Mourinho is a big fan of the Togolese striker and thinks he can get the best out of a player whose career at Eastlands has nosedived under Roberto Mancini. Real want to take Adebayor on loan until June 30 with the option to buy.
No 1 priority: Mourinho is keen to land the services of a new striker in January
Another City player who could boost Real's striking options is Tevez.
Mourinho was alerted to the forward's request to leave the club earlier this week and Real are confident Valdano can persuade fellow Argentine Tevez to move to Spain rather than join Chelsea.
The asking price could be a problem, with Real determined not to pay more than 15 million euros (£12.7m) for a player they think will only decrease in value.
The most surprising name on Mourinho's list is Hernandez. The 22-year-old has made an excellent start at Old Trafford since joining in the summer from Guadalajara for £7m and has impressed Mourinho.
Although he knows it is highly unlikely that United boss Sir Alex Ferguson will let the Mexican leave, Mourinho is willing to test his resolve with a 25m euro (£21.1m) bid and even offer Lassana Diarra on top.
Fair trade: Mourinho is willing to offer cash plus Lassana Diarra in his attempt to lure Hernandez from Old Trafford
Madrid are expected to start making enquiries soon with Mourinho needing a forward urgently to try to overturn Barcelona's two-point lead in La Liga.
Tevez must stay! Together we can make City great, Mancini tells captainReal Madrid line up Johnson as Jose rages at Bernabeu defender RamosMourinho on collision course with Real after calling for cash to land strikerMANCHESTER CITY FC