Sky reports that the Brazilian has reached an oral agreement with the newly promoted side over a loan without a purchase option, with the two clubs still working through the finer details.
Arthur is contracted at Bayer Leverkusen until 2031, but with regular football hard to come by, having largely been restricted to a squad role in recent seasons and repeatedly troubled by injury, a temporary switch to the Elbe looks set to give him the game time he needs.
The move would complete a significant overhaul of Leverkusen's right side. Guéla Doué is expected to arrive as a new first-choice right-back, Axel Tape looks likely to join Levante on loan, and Arthur's departure would leave the club with a settled long-term option while giving the Brazilian a fresh start elsewhere.
Werder Bremen had also shown interest in Arthur earlier in the window but appear set to miss out.
Notably, Hamburg are simultaneously closing in on a deal for another right-back, Zakaria El Ouahdi of Belgian side KRC Genk, with the two clubs believed to have reached a basic agreement over personal terms after Hamburg submitted their second offer for the Morocco international.
Whether the Bundesliga new boys ultimately need both players for the same position remains to be seen - currently Bakery Jatta, 28, is the club's only established option on the right side of defence. With the transfer window closing at 8pm on Tuesday, clarity on both fronts is expected by then at the latest, and Hamburg's willingness to pursue two options simultaneously underlines how urgently sporting director Claus Costa wants the position resolved before deadline day.
El Ouahdi, who has interested Leverkusen and Stuttgart at various points this window before both clubs looked elsewhere, is seen as the more expensive, long-term investment of the two targets, while Arthur represents the cheaper, short-term fix that would allow him to return to Leverkusen next summer once his loan expires.
Genk have so far knocked back two Hamburg offers, and a third improved bid is understood to be in preparation as the club tries to force through a deal before the window shuts.