The Croatian playmaker joined Barcelona last summer from Sevilla but has had his role in the squad called into question after being left out of big matches against Real Madrid and PSG.
El Mundo Deportivo reported that the two English sides inquired about the 26 year-old, asking if missing out on first team football was enough to convince him to leave the Nou Camp.
Rakitic decided to stay put but Arsenal in particular are thought to be keen to try again in the summer.
By Phil Wellbrook