But with Dundee United and Rochdale refusing to budge on their seven-figure asking prices for Craig Conway and Craig Dawson, respectively, Strachan could face a nervous end to the month to see if he lands his men before the transfer window shuts.
Ideally, the Boro boss will have made the necessary adjustments to his squad before Ipswich Town arrive at the Riverside Stadium to open the new season on Saturday, but that is looking increasingly unlikely.
Despite making five signings already this summer, Strachan has repeatedly highlighted during pre-season that this squad is not as big as everyone thinks it is and he is still actively pursuing a list of players.
And while he hopes chief executive Keith Lamb can persuade Conway and Dawson's employers to significantly lower their valuations, Strachan is also keen to bring in at least one new full-back.
It has emerged that Middlesbrough are hoping to convince Birmingham City to allow Hartlepool-born Murphy, a Boro Academy graduate who moved on under Steve McClaren, to move back to the North-East on loan.
Tottenham's Kyle Naughton, who spent last season on loan on Teesside, is also a candidate, but Strachan knows all about Murphy, who was outstanding during his time with Hibernian in the Scottish Premier League prior to his switch to St Andrew's.
Matthew Bates performed solidly in that role in the 2-2 draw against Union Berlin on Saturday, while Scott McDonald found his form just seven days before the campaign is due to start.
McDonald hit two goals in the final four minutes of the second half to cancel out a two-goal advantage the German Bundesliga 2 counterparts.
Berlin scored their first goal in the fourth minute when Chinedu Ede directed his header beyond Brad Jones from Ahmed Madouni's centre and Karlin Menyamina struck the second half an hour later.
But after a slow start in front of more than 10,000 supporters 100 of which were from the North-East Middlesbrough responded, picked things up and were level before the break.
McDonald's first was stunning, finding the roof of the net after turning in space and unleashing an unstoppable drive from 30 yards in the 41st minute. And then then he added his second with the last attack of the first half. Bates, again superb after his long battle to recover from injury, picked out his team-mate with a fine long pass. McDonald's first touch was precise before rounding the keeper to score.
There were no further goals during a slower-paced second half, but Strachan will be monitoring the fitness of Kris Boyd, who again had to be replaced through injury, although this time it was blisters.
Strachan also hopes Nicky Bailey will be fit for the start of the season. The £1.2m buy from Charlton had to sit in the stands in Berlin nursing a knock.
Boro's latest signing, Tarmo Kink, meanwhile, has insisted he has the mental and physical toughness to succeed in he English league.
Kink, aware of interest from German outfit Kaiserslautern, completed a switch from Hungarian club Gyori ETO last week and there have been claims in his Estonian homeland that he might not have the style to turn it on in the Championship.
I have been written off by people in Estonia before and proved them wrong, he said.
The doubters are already questioning whether the fast and physical game in England is not suitable for me. I will show them I'm strong enough.
MIDDLESBROUGH (4-4-2): Jones; Hoyte, McManus, Wheater, Bates (Bennett 75); Robson, Arca, Thomson, Flood (Williams 75); McDonald (Lita 75), Boyd (Miller 79).
Subs (not used): Coyne (gk), Grounds, Franks.
Source: Northern Echo
Source: Northern Echo