French outlet Le Point claims Monaco are prioritising a central defender in their attempts to escape the Ligue 1 relegation zone.
And current Gunners captain Laurent Koscielny is reportedly the name that keeps coming back 'most insistently' in that regard.
Henry's side has conceded 29 goals so far this season, with only three other clubs letting in more.
Meanwhile, Henry is also 'particularly' interested in signing Cesc Fabregas to fill a gap in midfield created by the departures of Fabinho, Moutinho, Bakayoko and Bernardo Silva in recent seasons.
The 2010 FIFA World Cup winner, who has attracted the interest of AC Milan, already knows Monaco sporting director Michael Emenalo, who brought him to Chelsea and he only has six months left on his contract.