Boro, last night boosted by the news that striker Kris Boyd's injured ankle is nothing more than a bruised fibulam, are not prepared to match the valuation after already agreeing to sign five players this summer at a cost of more than £5m, by far the most spent by a Championship club this summer.
The two clubs have been in discussions for a number of weeks over Conway, with Strachan revealing during the club's trip to Ireland that he has further talks planned about new signings before the squad head out for a tour of Germany on Tuesday.
There has been little progress made towards a deal for Conway, but Middlesbrough will be doing their best to ensure Strachan lands his man before the visit of Ipswich on August 7.
The 25-year-old is exactly what Boro are looking for as he can play on either flank and Strachan's other main wing target, Andrew Driver, is being priced out of a move to the Riverside Stadium with Hearts' £3.5m fee.
Strachan would prefer to land them both, but for now he would be satisfied if chief executive Keith Lamb can strike a deal with Dundee United quickly. So far, however, they haven't made an official offer.
Nevertheless, Middlesbrough hope a deal can be struck for around £700,000 sooner rather than later.
Strachan intends to step up his pursuit of the three or four more players he wants to add to his squad before travelling out to Germany for friendlies with Sashen Leipzig on Wednesday and Union Berlin a week today.
But he has been warned by Rochdale not to expect them to budge on their £1m asking price for highly-rated defender Craig Dawson.
Despite the 20-year-old welcoming a move to Teesside, Dale manager Keith Hill said: The fact is our valuation of Craig hasn't been met by any club and it will be Middlesbrough's loss when he goes and signs for another club that will meet Rochdale's valuation.
Despite encouraging signs from Middlesbrough's new faces in their opening two matches of pre-season against Athlone Town and Bray Wanderers, more money will be spent on the squad in the next few weeks.
Julio Arca said: We have signed a big striker in Kris Boyd, a good central midfielder in Kevin Thomson and three others.
The manager will be looking for a few more, I'm sure.
He is still working on that.
Boyd, meanwhile, was relieved last night when a scan on his ankle revealed nothing more than bruising and he will travel to Germany with the squad.
Boro defender John Johnson, 21, has signed a two-year deal with Northampton following a successful loan spell at Sixfields last season.
Source: Northern Echo
Source: Northern Echo