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But Heynckes, speaking ahead of Bayern’s Champions League quarter-final first leg in Seville, ruled out the prospect of Bayern striker Robert Lewandowski heading in the opposite direction and moving to Real this summer.
James agreed to a two-year loan when he joined Bayern from Los Blancos last year and the Colombian has been in excellent form this season.
A number of top clubs are reportedly interested in buying the 26-year-old, but Heynckes, who is set to retire at the end of the season, believes he will stay at Bayern.
“He’s happy in Munich and at Bayern,” Heynckes said on Monday.
“Logically I think he’ll stay next year and after. Bayern must take a decision about when they buy him.”
Real signed James from Monaco in a deal worth 90 million euros ($110.6 million) after he was one of the stars of the 2014 World Cup.
But he struggled to live up to expectations in Madrid and has only rediscovered his best form under Heynckes, who returned as Bayern manager in October.
“He wasn’t in the right physical shape. Every player needs to be at their maximum,” Heynckes said.
“We talked about many things, but now he’s got lots of confidence from me and that shows in how he’s performing, both physically and technically.
“Now he’s a different player.”
— Real’s wishlist —
According to reports in Spain, Lewandowski is high on Real’s wishlist after scoring 40 goals in 42 games this season.
“(Bayern chief executive) Karl-Heinz Rummenigge spoke last week and said Lewandowski was going to play at Bayern next season,” Heynckes said.
“I do not give Real Madrid any chance of signing Robert Lewandowski.”
Against Sevilla, Bayern will as strong favourites to reach the last four.
But Sevilla are a dangerous opponent, having knocked out Manchester United in the last 16 and drawn 2-2 with unbeaten Barcelona in La Liga on Saturday. Barca scored twice in the last three minutes.
“The best example is the Barca game,” Bayern midfielder Javi Martinez said.
“Sevilla played well, they were compact, they were superior to Barca in my opinion. You can’t relax against Barca, they can score at any time, but they were superior.
“They knew how to play against them and that teaches us to be 100 per cent for the whole game.”
While Bayern are attempting to reach their sixth Champions League final in seven years, this is Sevilla’s first ever appearance in the last eight.
Asked if his side were motivated by making history, Sevilla coach Vincenzo Montella said: “I think we’ve already done it, right? But personally I think we are not satisfied with this.
“We are going to try to do it in front of our own supporters and that will be a great help. We will fight to the death, until the end.”
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