The Latvians overcame The New Saints in the same competition last season on the away goal rule following a 4-4 aggregate.
Following the draw Llanelli striker Rhys Griffiths said: "It's a draw that we feel we can win.
"We can learn a lot from TNS and I'm sure that Peter Nicholas will contact former TNS manager Ken McKenna and other people to ask them about their strengths and weaknesses.
"If we prepare properly, we'll have a chance and that's really all we can ask for.
"It's hard being in Wales with our close season but more than anything I hope that our preparation continues, which so far has been as good as it could.
"So if that carries on, we can have no excuses."
Tickets for Llanelli's home game are due to go on sale at Stebonheath Park on Thursday between 1000 and 1900 BST to season ticket holders, patrons and supporters club members.
Voucher holders from the WWFA Senior Cup Final and Under-19 game against Carmarthen will be able to buy tickets from 1000 BST on Friday with the remainder going on general sale from 1100 BST on Saturday.
2008/09 Uefa Champions League first qualifying round
Linfield (Northern Ireland) v Dinamo Zagreb (Croatia)
Valletta (Malta) v Artmedia (Slovakia)
Dinamo Tbilisi (Georgia) v NSI Runavik (Faeroe Islands)
Santa Coloma (Andorra) v Kaunas (Lithuania)
Murata (San Marino) v IFK Goteborg (Sweden)
Llanelli (Wales) v Ventspils (Latvia)
Anorthosis Famugusta (Cyprus) v Pyunik (Armenia)
Inter Baku (Azerbaijan) v Rabotnicki (Macedonia)
Tampere United (Finland) vs. Buducnost Podgorica (Montenegro)
F91 Dudelange (Luxembourg) v Domzale (Slovenia)
Dinamo Tirana (Albania) vs. Modrica (Bosnia-Herzegovina)
Aktobe (Kazakhstan) vs. Sheriff (Moldova)
Drogheda United (Rep of Ire) v Levadia Tallinn (Estonia)
BATE (Belarus) v Valur Reykjavik (Iceland)
First leg ties to be played 15-16 July, second legs on 22-23 July
2008/09 Uefa Champions League second qualifying round
Rangers (Scotland) v Santa Coloma-Kaunas winner
Brann (Norway) v Llanelli-Ventspils winner
Inter Baku-Rabotnicki winner vs. Partizan Belgrade (Serbia)
Tampere United-Buducnost Podgorica winner v Artmedia-Valletta winner
Anorthosis Famugusta-Pyunik winner v Rapid Vienna (Austria)
F91 Dudelange-Domzale winner v Dinamo Zagreb-Linfield winner
Panathinaikos (Greece) v Dinamo Tbilisi-NSI Runavik winner
Murata-IFK Goteborg winner v FC Basel (Switzerland)
Aktobe-Sheriff winner v Sparta Prague (Czech Republic)
Drogheda United-Levadia Tallinn winner v Dinamo Kiev (Ukraine)
Anderlecht (Belgium) v BATE-Valur Reykjavik winner
Beitar Jerusalem (Israel) v Wisla Krakow (Poland)
Fenerbahce (Turkey) v MTK Budapest (Hungary)
Aalborg (Denmark) v Dinamo Tirana-Modrica winner
First leg ties to be played 29-30 July, second legs on 5-6 August
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