Marca claims that Morata, who reportedly wants to leave Madrid this summer after failing to earn a starting place, has an offer from United and that his agent met with the Spanish club's executives at the Santiago Bernabeu on Wednesday to discuss his departure.
Ex-Middlesbrough manager Karanka, who was an assistant to Jose Mourinho at Madrid from 2010 until 2013, knows Morata well and when asked about the Spain international's link with United, he told Cadena Ser: "Alvaro fits anywhere.
"We knew [about his talent] since he was with us at the age of 19 and I have known him since he was 17 because he came to the Under-17 World Cup in Nigeria [with a Spain team Karanka coached].
"Alvaro is the classic player that can fit anywhere. He has everything. For this [Premier League] football, he is a spectacular player."
The two clubs have yet to agree terms with Marca reportedly claiming that Madrid will only sell Morata for €90 million, a figure that United are not prepared to pay.
Alvaro Morata has been linked with a move to Manchester United.
Morata returned to Madrid last summer after two impressive seasons with Juventus and is under contract with the European champions until June 2021.
"The time he spent at Juventus was great for him to mature," Karanka said.
However, the 24-year-old earned just 14 La Liga starts under Madrid coach Zinedine Zidane last season.
He made the most of his opportunities, scoring 15 goals and setting up four more in 26 league appearances. In the Champions League, in which he came off the bench eight times and made just one start, Morata found the back of the net three times.
Earlier this month, Morata stated his wish to play more knowing there will be plenty of competition for places in Spain's squad for next year's World Cup.
He told Marca: "Next year there is a World Cup. I want to play and be important in my team."
A move to United would see Morata reunite with former Madrid coach Mourinho, who gave the player his first-team debut in August 2010.