At the weekend, manager Walter Smith said the bank was effectively operating the club and that all of his players have been up for sale since January.
However, a statement from the bank on Monday afternoon read: "We do not run or manage the companies that we bank - that is, quite properly, the responsibility of the management.
"We would therefore like to be clear that Rangers FC is neither operated or run by Lloyds Banking Group."
The statement also made it clear that it was not behind Murray's decision to step down as chairman.
"The board of Rangers FC is developing and implementing a sustainable business plan and we have agreed to support this plan," it stated.
"The group is aware of the unique position that football occupies across many Scottish communities and has been working with Scottish football clubs, including Rangers."
Rangers say Murray is "considering options" regarding his shares and South Africa-based businessman Dave King has been widely linked with a possible interest in significantly increasing his stakeholding.
However, they stressed Murray's considerations are still at an early stage and "this may or may not lead to MIH disposing of some or all of its stake in the club to a third party".
On the question of selling the club, Lloyds says that this is a decision for the board and that the bank will only play only the normal role for a creditor in any such sale.
Lloyds does not hold any equity in Rangers and it is understood that the share ownership has not changed since Murray stood down.
Our boys have handled the situation well and did extremely well last season to win the league and the Scottish Cup
Smith told BBC Scotland on Saturday that Rangers were facing difficult times.
"Now the bank have taken over the running of the club, they'll have their own ideas and obviously investment isn't one of them," Smith said.
"I just think there's a stagnation about our club at the present moment."
Smith's contract, and that of assistant boss Ally McCoist, expire in January, midway through the current season.
However, with the current financial uncertainty, it is unclear whether new chairman Alastair Johnston will offer them new deals before the turn of the year.
Rangers drew 1-1 with Hibernian at Ibrox on Saturday and lost heavily to Unirea Urziceni in the Champions League in midweek.
And Smith, who refused to elaborate further at a Rangers media conference on Monday, admitted on Saturday that he was unable to bolster his squad.
"Rangers' situation is quite simple and we've been fairly honest about it for about a year now," he said.
"All the players have been up for transfer. If anybody is telling me that's a motivational factor for any player then they're living in another world from me.
"Our boys have handled the situation well and did extremely well last season to win the league and the Scottish Cup.
"There are things that are outwith everyone's control. David Murray has been fantastic for Rangers over his 20 years. He's had to step away and now the bank have taken over the running of the club.
"So, therefore, we sit and wait for an owner. The club's been up for sale for a period of time and I don't think all those things going on have helped."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.