Koeman's Everton revolution is now in full swing after a tricky patch earlier in the season, with the Toffees now running 20km more per game than they were at the beginning of the campaign. Osman praised the former Southampton manager's work on Merseyside but, like many Evertonians, he is wary of potential interest from the Catalan giants.
"It's not surprising he's been linked with Barcelona," Osman told Sky Sports. "He's such a massive player on a world scale, he played for Barcelona. He's doing really well at Everton at the moment with the run of fixtures and form they've shown and it's no surprise that he's being linked with the job.
"It would be disappointing from an Everton perspective if he were to leave now with things looking positive and moving in the right direction, but it's difficult if Barcelona come knocking. I hope [that he stays with Everton]. He's going about things fantastically well at Everton and it would be disappointing if things changed."
Koeman's name has long been linked with Barcelona and the rumours are set to intensify after Luis Enrique announced that he will leave his position as boss of the Blaugrana at the end of the season. The Barcelona legend has experience of managing in La Liga with Valencia but is not seen as one of the frontrunners for the position in Spain, with Athletic Bilbao's Ernesto Valverde and Sevilla manager Jorge Sampaoli the two current favourites.
Koeman could well have a big decision to make about his future in the summer but his immediate focus is on Everton's trip to Tottenham. The Toffees are unbeaten in the Premier League in 2017 but will be facing a Spurs team that has not tasted defeat at White Hart Lane this season.