From the Wikipedia page 
Ludgate Circus tube station was planned in the 1970s to be built as part of phase two of the London Underground's Jubilee line near Ludgate Circus. Preliminary preparation work was begun before the plan was postponed due to lack of funds. When the Jubilee line was extended in the late 1990s, it took a different route south of the River Thames and the phase 1 portion of the line from Green Park to Charing Cross was taken out of passenger use.
A National Rail station was eventually constructed on the site, but to serve the north-south Thameslink route, rather than the originally envisaged east-west line. Also, the station was not named Ludgate Circus, but rather St Paul's Thameslink, later changed to City Thameslink due to confusion with the nearby St Paul's Underground station. It was however built in such a way as to allow for an underground east-west aligned station to be easily integrated; this can be seen in the wide spaces on the Ludgate end of the station, where large doors open on to a corridor intended to lead to escalators to a Underground concourse level. It is still known today as the LUL corridor by staff.
There are no plans or even suggestions to build a tube station at Ludgate Circus. However there are long term proposals to build an extension to the Docklands Light Railway from Bank station to Charing Cross, with DLR stations planned to be included at Ludgate Circus and Aldwych