The Ibrox side will face a Spurs XI in a closed-door fixture at the Tottenham training ground during a trip to London.
Among those who could line up for Rangers are former Manchester City and Doncaster full-back Reece Wabara, ex-Livingston, Middlesbrough and Bradford City midfielder Andy Halliday and Northern Ireland youth international midfielder Jordan Thompson who has just been released by Manchester United.
Veteran former Derby County midfielder John Eustace is also training with Rangers this week, although he is still recovering full fitness following a serious knee injury.
Rangers assistant manager David Weir has admitted to a degree of anxiety over the progress of the player recruitment drive ahead of the new season but insists they cannot afford to rush the rebuilding of their squad.
Just over three weeks after Mark Warburton was appointed Rangers manager, with Weir as his right-hand man, only three new signings have been completed so far in goalkeeper Wes Foderingham and defenders Danny Wilson and Rob Kiernan.
Warburton and Weir inherited a significantly depleted first-team pool following the release of 11 senior players at the end of last season’s failed bid for promotion from the Championship.
“I wouldn’t say we’re relaxed about it because it’s a really important part of the job,” said Weir. “You need good players to be successful and we’re very clear on the fact we need to get new players in.
“We know there have to be additions but we want good quality additions and players who will help Rangers for a long time. Part of the reason we’ve got the job is perhaps because we know a different market from the one Rangers may have been used to. We’ve been working in the Championship and we know that league well. That’s probably the market we are looking at but we’re conscious of making good decisions and doing our homework with regard to new signings.
“Ideally we want to see those guys who are training with us just now in a match situation and that works both ways.
“They’ll want to have a look at us too. Hopefully we can have a look at them this week and we’ll take things from there.
“It can’t be an indefinite thing because the players coming here on trial are looking for a contract. But we need to make sure they are right for the club, so we’ll judge them after a game.
“After Tottenham on Friday, we will have another closed door game next week and then the friendly against Burnley at Ibrox on 21 July.
“Mark and I came in relatively late so we are happy with the pre-season plans we have in place.”
Weir, speaking at the launch of Rangers’ public sale of season tickets after more than 22,500 supporters renewed for the 2015-16 campaign, expressed his delight at the response he and Warburton have received from the players already under their command.
“They’ve worked very hard and they’ve bought into the ideas we’ve been trying to put across and the way we want to work so far,” added Weir.
“I couldn’t fault the players because their effort and level of football has been first class. It’s been full on since we started.”
Among the many strands of criticism levelled at Rangers last season was a perceived lack of fitness and sharpness in their performance levels.
Last week, Jim Henry left his post as head of athletic performance and sports science at the club, along with coach Gordon Durie as Warburton and Weir reshape the backroom staff.
“We have to put our own stamp on that,” said Weir. “We have to work within our own parameters. Gordon has been a great servant to Rangers but it was just a case of his role coming under what Mark and myself do.
“We do the majority of the coaching ourselves. So it was just a matter of trying to streamline it as much as we can, getting people to work in the right areas.
“Gordon was great, he was in here with us for the first week and worked really well with us. But it’s just not really a role we use.
“We are in discussions over the role Jim Henry had. We are trying to make the right decision on that. We have people already here who are working well, so you would like to give them the opportunity as well to show they are worthy.
“Fitness is a big factor for us. I can’t comment on last season, because I genuinely didn’t see a lot of Rangers games.
“All I can say is that fitness is fundamental to playing football in the modern age. All of our training sessions are intense. They are measured with set periods of time assigned to getting players to the fitness level we believe is needed.
“We have done that in the past couple of years with similar methods at Brentford and have had decent results.
“We are pretty sure that what we do works. We scored a lot of late goals and keeping players on the pitch in good condition is a big part of that.
“A dynamic style of play is ideally what we want. We have youth and energy in the squad and people want to see effort.
“Rangers fans are renowned for wanting desire and energy from their team. We need to have players who are capable of producing that week in, week out.”