With Gary O'Neil expected to leave the Riverside this summer, Strachan will make midfield improvements a priority as he attempts to assemble a squad capable of mounting a sustained promotion push next season.
He has already identified a number of targets, with 24-year-old Conway featuring prominently on his wanted list.
Tellingly, a Middlesbrough scouting party travelled to Motherwell on Sunday to watch the midfielder score Dundee United's third goal in a 3-2 win at Fir Park.
They will have watched Conway bolster an already impressive reputation that has seen him emerge as one of the most highly-rated players in the Scottish Premier League this season.
Equally at home on either flank, the Irvine-born winger has scored ten goals in 110 games since joining Dundee United from Ayr United in 2006.
He is almost certain to leave Tannadice this summer, but a recently-signed contract extension means his current deal is not due to expire until 2011. As a result, Dundee United officials will almost certainly demand a seven-figure fee for his services.
Whether Strachan is prepared to pay that remains to be seen, but the Boro boss is unlikely to have things all his own way as Rangers boss Walter Smith is also known to be an admirer.
Smith has been linked with both Conway and fellow Dundee United midfielder, David Goodwillie, in recent weeks, and while money is currently tight at Ibrox, the former Everton manager is expected to have money to spend this summer.
Boro will be able to match whatever contract offer Rangers place on the table however, and having persuaded the likes of Barry Robson and Scott McDonald to move south in January, Strachan will hope to convince Conway that a transfer to Teesside offers him a route to the English top-flight.
Meanwhile, the administrator in charge of Portsmouth has revealed Boro paid more than £500,000 to enable O'Neil to make his 100th appearance for the club.
The skipper played at West Brom on Saturday after a compromise was agreed with Pompey officials, and details of the deal, which will also allow O'Neil to face Coventry and Leicester in the final two games of the season, have now been disclosed.
"We came to an agreement eventually, although we have to keep the details confidential," said Portsmouth administrator Andrew Andronikou.
"However, they have paid us more than £500,000 and both sides are happy with that."
* Boro season card holders can claim two free Under-18 tickets and two adult tickets priced at £5 each for Saturday's final home game with Coventry.
Season card holders will also receive 20 per cent off all merchandise at the MFC official stores on production of their season cards on Saturday.
In addition, all season card holders who apply for friends and family tickets will be entered into a prize draw to win a VIP training experience with Boro's first-team squad.
Season card holders wanting to claim their free or 5 tickets should download and complete an application form from Boro's official website at www.mfc.co.uk.
They should then produce their season card, along with their completed application and, if applicable, any payment, at the Riverside ticket office or the ticket facility at the MFC store in Captain Cook Square.