Steve Cooper is keen on strengthening his Swansea side as they aim to get promoted to the Premier League this season, wanting more options up front.
Swansea failed in their pursuit of Southampton forward Michael Obafemi, and have now turned their interest towards Balogun.
This season, Balogun has made just five first-team appearances under Mikel Arteta, all of them coming in cup competitions, and he will be keen for a move for more regular playing time.
The 19-year-old has impressed in his appearances, scoring twice in the UEFA Europa League group stages, against Molde and Dundalk.
Swansea have reportedly made contact with Arsenal regarding a potential loan deal for the young forward until the end of the season.
Last season, Arsenal rejected £5 million bids from Brentford, with the striker's contract ending at the end of the season.
Swansea have been very impressive this season, but they have struggled to score, with Andre Ayew and Jamal Lowe their two greatest goalscorers this season, with on loan forward Viktor Gyokeres failing to settle and young Liam Cullen being barely used.
Whilst Swansea have been excellent defensively, conceding just 13 goals in 23 Championship games, they have only scored 27 goals in the league this season, the least out of the top five.
Swansea have done excellently with most loans in the past, with Morgan Gibbs-White, Rhian Brewster and Marc Guehi all doing very well at the club in recent years.
Swansea will have to move fast however, with Balogun having the possibility of signing for non-English clubs on a pre-contract this month.