Osimhen, 26, has been in outstanding form for Galatasaray, scoring 19 goals and providing seven assists this season across all competitions.
He broke his arm in the Champions League round of 16 against Liverpool following a challenge from Ibrahima Konaté in March and only returned to action this week, playing 20 minutes in a Turkish Cup defeat to Gençlerbirligi.
Halis placed both Spanish clubs firmly in the picture. "His signing could be between Real Madrid and Barcelona. One has given up on Lewandowski.
"The other has no centre-forward. Real Madrid have not had a true number nine since Karim Benzema's era. They are forced to field MbappĂ© and VinĂcius as forwards.
"If they sign Osimhen, MbappĂ© and VinĂcius will play in their natural positions as wingers and will be more effective. VĂctor Osimhen would be a very functional player for Real Madrid."
Barcelona face a budget constraint ahead of any move. According to Africa Foot, that is the reason behind the club's decision to part ways with Jules Koundé, Ferran Torres, Frenkie de Jong, Robert Lewandowski and Marc Casado this summer to create financial room.
Galatasaray are expected to demand more than the âŹ75 million they paid Napoli last summer, with any bid needing to clear âŹ100 million to open serious negotiations.