Great Britain showjumping chief Rob Hoekstra says he is "extremely close" to finalising the team for London 2012.
Final deliberations between Hoekstra and his fellow selector Di Lampard are set to take place next week, after which a four-strong contingent and possibly two reserves will be announced.
Britain finished sixth in the latest Nations Cup round in Rotterdam on Friday, a performance highlighted by Scott Brash and Peter Charles jumping clear rounds on Hello Sanctos and Murka's Vindicat W, respectively.
But there was major disappointment for 2008 Olympian Tim Stockdale, whose selection hopes appear to have dipped after collecting 17 faults in round one on Fresh Direct Kalico Bay, and then eight in the second round.
Northamptonshire-based Stockdale broke his neck last October when he fell from a horse he was trying out in north Wales. But he returned to Nations Cup action in Switzerland three weeks ago by recording two clear rounds, and then finishing second in the St Gallen grand prix two days later, before gaining another opportunity to impress Hoekstra in Rotterdam.
The fourth team member, Tina Fletcher, posted five faults in each round aboard Hello Sailor as Olympic team gold medal favourites Germany took top spot, ahead of Sweden with France third and Ireland fourth.
Brash, world number three Nick Skelton and Ben Maher are expected to gain London places, but the fourth spot appears to still be wide open, with Charles perhaps now a marginal favourite.
"It has been a very interesting day for us, and it has provided a few good headaches from a selector's point of view," Hoekstra told Press Association Sport. "We have seen our riders competing under extreme pressure, and we have seen some good performances.
"It was always our intention to give riders the opportunity to show us what they could do in the ring, and we are extremely close to putting together a very strong team for the Olympics.
"We have a number of riders that weren't here in Rotterdam but are also in strong contention, and we will look at things collectively."