Harlequins, Connacht, Bayonne and I Cavalieri Estra each have one win apiece after the opening two rounds, with just two points separating top and bottom in the tightest Amlin Challenge Cup pool.
Elwood, who scored 473 points during his playing career with Connacht said: "Conor and I played together at club level for Lansdowne in Dublin and also for Ireland, so I guess we know each other inside out.
"He was a great professional as a player and a great student and analyst of the game who understands the sport from top to bottom.
"From the outside, he seems to have adapted to his new role at Harlequins really well, bringing to bear his good man-management skills.
"He is a tough task master who will bring an enormous amount to their team - and get the best out of them - and I am really looking forward to meeting up with Conor again."
He added: "Harlequins are a strong team playing in a very competitive Premiership and are very well coached by John (Kingston). They are a well organised and disciplined team under him and will certainly be a great test for us.
"We are under no illusions regarding the huge challenge we face at the Stoop - both collectively as a young team and for me as a young coach - but it is one we are really looking forward to.
"We have met them a fair few times in this tournament so we know each other pretty well."
Connacht were forced to call off their Magners League match against Aironi Rugby last weekend due to the adverse weather conditions, and go into these two contests with Harlequins on the back of four straight defeats since beating Bayonne 16-13 in the Amlin Challenge Cup back in October.
"Obviously we would far preferred to have had the game against Aironi go ahead because it was an important game for us to try and maintain the performance levels we had produced against the Ospreys and Edinburgh in our last two matches," admitted Elwood.
"The performances in both those games were right up there - but we are simply not winning matches we really could win.
"In the nine Magners League matches we have played so far, we genuinely could and should have won three of the ones we lost.
"Quite simply we are not closing out tight games and that is something we must get right because that would then generate confidence in the team for the rest of the season."
Connacht have played more Amlin Challenge Cup matches than anyone else, taking part in all 15 tournaments to date, but Elwood would love the team to taste Heineken Cup action.
"We do have a proud history in the Amlin Challenge Cup and we are quite happy with our record there, but obviously we would like not to be forever regulars and gain qualification for the Heineken Cup."