Yes, there were plenty of efforts by the "white" boxing establishment to match Johnson with Langford. Especially in places like England, France, and Australia. The old Aussie promoter, Hugh McIntosh, was most prominent when it came to offers and he made numerous of them to Johnson in which he would have been well compensated for the time.
There were efforts made in the US as well, but if I'm remembering right, the closest it came to happening on American soils was one night when both were at a boxing event in Boston I think it was. Both agreed to a future fight there on the spot while appearing in the ring together in front of the live crowd, and both agreed to post a forfeit with a local newspaper within a short time span. Langford, who I don't believe had the money, refused to post the forfeit until Johnson did, and Johnson refused the same. That's about the closest Johnson had shown to a willingness to face Langford again. Johnson did have a signed agreement to face Langford in England in 1909, but he wasn't sincere and never intended to honour the commitment in the first place.
And a Johnson-Langford rematch for the title would have drawn quite well in places like France and Australia. Maybe even England too. In the US, who the hell knows since hardly anybody was drawing well in boxing at the time in the 1910's regardless if it was white vs white, black vs white, or black vs black. The public lost most of it's trust in boxing on the east coast a decade before that, and then mostly dried up on the west coast when the popularity shifted out there soon after. Boxing's image was greatly repaired after WW1 when the American public learned of all the boxers that served and taught their sport to the soldiers during the war. Boxers weren't viewed as scum anymore and instead started to get celebrated. Then you had a promotional genius like Tex Rickard to further enhance that image change and use his power to influence fans and legislators alike into becoming even more accepting of the sport. And of course Rickard had an attraction like Dempsey who Rickard could initially promote as the villian per se and convince the public to pay big money to see somebody beat him. But the 1910's was a terrible decade for boxing in America. The worst. The money, however much there was, was to be made was elsewhere around the world.