The newspaper claims the Manchester City manager has been monitoring Clarke's progress since the latter signed his first professional contract last year.
The 18-year-old made his Leeds debut earlier this season, under a man Guardiola once claimed to be the world's best coach - Marcelo Bielsa.
And he provided his first assist in United colours on Saturday, enabling Pablo Hernandez to settle their Yorkshire derby at Sheffield United.
Leeds are, however, under little pressure to sell Clarke, whose existing deal runs until 2021.
And the Whites' promising league position - four points clear of third-place West Bromwich Albion in second - could convince the Yorkshireman to remain at Elland Road.
That said, Manchester City are not the only Premier League club keen on Clarke, according to the Sun.
The City winger, Brahim Diaz, has been strongly linked with a move to Real Madrid this week.
Could Leeds lose Clarke to Manchester City?