Former Hammers youngster Johnson has been heavily linked with a return to Upton Park on a free transfer when his contract at Anfield expires his summer - per the Daily Mail.
Talk of a move surfaced as West Ham faced up to the hefty price tag and increased competition for Arsenal loan star Jenkinson, who has been a revelation for Sam Allardyce's side this season.
Well stocked in the right-back berth with the likes of Hector Bellerin bursting onto the scene, the Gunners are believed to want between £8-10 million for the flying full-back who has been first choice under Big Sam throughout the campaign.
In fact, Jenkinson's form for the Hammers has actually made life even more difficult for co-owners Gold and Sullivan to get him signed up permanently as it has alerted a number of top clubs at home and abroad to his quality and availability.
Johnson, who like Jenkinson is an England international, is believed to be actively seeking a return to his London roots and could pitch up for the club's final season at the Boleyn, 17 years after making his debut there.
While both players have immense quality, it is the younger charge Hammers fans want to see as their right-back next season and they clearly think the Gunner is worth the money being quoted.
That's according to the results of a poll we conducted on HITC where 89% of fans (343) said they wanted Jenkinson signed up permanently while just nine per cent (36) think the club should push through a move for their former Academy graduate.
The other two per cent said they didn't want either player to be the club's right-back next season.
It is easy to see the logic of the Hammers fans. With 54 England caps, Johnson offers more experience, a commodity Sam Allardyce recently admitted his side has lacked at times this season as they have tumbled down the league from fourth to midtable since Christmas.
But Jenko, as he is affectionately known, is only 23 and has his best years ahead of him while Johnson, at 30, probably doesn't.