The Ajax coach has been linked with the Geordies.
Lovenkrands told the Evening Chronicle: "I still think he would be a fantastic choice. I spoke to Ronald De Boer after Fernando Ricksen's testimonial.
"And he did say: 'Frank looks like he will probably stay at Ajax'.
"You look at it and he has Champions League with Ajax but this would be a new challenge. Frank De Boer would be an amazing choice.
"You can only try. I hope Newcastle try to get him. At least try and if he says no fair enough but I do think that he would be a perfect fit.
"I just hope the club take that step further and try to get him."