The possible arrival of the 21-year-old Santos striker has cast doubt on Owen's future in Madrid but Beckham said the former Liverpool striker had nothing to fear.
"Michael is established in this team, with the manager and with the fans," Beckham told Reuters after Monday's humbling 3-0 pre-season defeat by Japan's Tokyo Verdy.
"I'd like Michael to stay because one, he's a good friend and two, he's a great player."
But Beckham said he would welcome the arrival of Robinho, whose move to the Spanish club is being challenged by the Brazilian Football Confederation (CBF).
"He's a great player," said Beckham.
"From what Roberto (Carlos) and Roni (Ronaldo) say, he's one of the best young players in the world.
"I haven't really been looking at what's been going on and whether he's coming or going --
Real said last week that they had paid 60 percent, or $30 million, of the $50 million buy-out clause in Robinho's contract to buy Santos's share of his rights.
The player is anxious to join the nine-times European champions and has waived the remaining 40 percent to which he is entitled.
But the CBF said a unilateral breach of contract would require Real to pay Santos the full $50 million for the young Brazil international.
Owen was Real's second highest scorer last season with 13 league goals but has been frustrated by the amount time he has spent on the bench since arriving at the Bernabeu last year.
The England striker has been linked with a return to Liverpool and several other top English Premier League clubs.