The club have already signed two players – Matias Pellegrini and Julian Carranza – as they continue to make additions ahead of their first MLS campaign next year.
The Uruguay international, who has two years left remaining on his current deal at the Nou Camp, is reportedly interested in the Inter Miami project in the long term.
The 32-year-old has been hindered by injuries in the previous two campaigns and picked up another setback in Barcelona’s first La Liga game of the season last weekend.
Suarez had to be substituted after injuring his calf as Ernesto Valverde’s side lost 1-0 to Athletic Bilbao.
‘It is something which looks a really interesting project,’ he told talkSPORT.
Beckham was given a headache this week after a report found Inter Miami’s stadium site had twice the legal limit of arsenic contamination which could cost $50million to clean up.